Maths
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Responding to change (a2 only)
Infection and response
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Organisms respond to changes in their internal and external environments (a-level only)
Biological molecules
Organisation
Substance exchange
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Britain & the wider world: 1745 -1901
1l the quest for political stability: germany, 1871-1991
The cold war
Inter-war germany
Medieval period: 1066 -1509
2d religious conflict and the church in england, c1529-c1570
2o democracy and nazism: germany, 1918-1945
1f industrialisation and the people: britain, c1783-1885
1c the tudors: england, 1485-1603
2m wars and welfare: britain in transition, 1906-1957
World war two & the holocaust
2n revolution and dictatorship: russia, 1917-1953
2s the making of modern britain, 1951-2007
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Physics
21 Dec 2025
365
5 pages
Ever wondered why a gas heats up when you pump up a bike tyre, or why absolute zero... Show more
Think of internal energy as the total energy stored inside any object - it's basically all the kinetic and potential energy of every single particle added together. The kinetic energy comes from particles buzzing about randomly (especially noticeable in gases), whilst potential energy comes from how these particles interact with each other.
What's brilliant about internal energy is that it depends entirely on the state of your object. Change the temperature, pressure, or volume, and you'll change the internal energy too. Here's the key bit adding heat to a system always increases its energy, but that doesn't necessarily mean the temperature goes up every time.
For ideal gases, life gets much simpler because we assume the particles don't interact with each other. This means they only have kinetic energy, no potential energy to worry about.
Quick Tip Remember that internal energy is about the total energy of all particles - not just the average!
The internal energy of an ideal gas follows the equation U = (3/2)nRT, where n is the number of moles, R is the gas constant, and T is temperature in Kelvin.
Specific heat capacity tells you how stubborn a material is about changing temperature - it's the energy needed to warm up 1kg of something by just 1K. Water's particularly awkward with a massive specific heat capacity of 4180 J/kg·K, which is why it takes ages to boil a kettle!
The equation Q = mcΔθ is your best friend here. Q is the heat energy, m is mass, c is specific heat capacity, and Δθ is the temperature change. Pretty straightforward once you get the hang of it.
Latent heat is completely different - this is energy that goes into changing state (like melting or boiling) rather than changing temperature. You've got latent heat of fusion (solid to liquid), vaporisation (liquid to gas), and sublimation (solid straight to gas).
The Kelvin scale starts at absolute zero where particles theoretically stop moving completely. The brilliant thing is that 1K = 1°C in terms of temperature differences, so conversions are dead easy.
Remember At absolute zero, gas particles have no kinetic energy and exert zero pressure!
The kinetic theory makes some clever assumptions about ideal gases that make the maths work beautifully. Particles are tiny compared to their container, they only interact during perfectly elastic collisions, and they're constantly moving in random directions.
This leads to the classic gas laws you need to know pressure is proportional to temperature , pressure is inversely proportional to volume (Boyle's law), and volume is proportional to temperature (Charles' law). These all combine into the relationship PV/T = constant.
Pressure in gases comes from particles smashing into container walls and changing momentum. When a particle hits a wall, it experiences a momentum change of 2mv (since it bounces back). This constant bombardment creates the steady pressure you can measure.
Key Insight Gas pressure is literally millions of tiny molecular collisions happening every second!
The rate of momentum change gives you force, and force per unit area gives you pressure - it's that simple.
A mole is just Avogadro's number (6.02 × 10²³) of particles - think of it as chemistry's way of counting ridiculously large numbers. One mole of any substance has a mass in grams equal to its relative atomic or molecular mass.
The ideal gas equation comes in two handy forms PV = nRT (using moles) or PV = NkT (using actual particle numbers). R is the molar gas constant and k is Boltzmann's constant .
These constants are related by R = kN_A, which makes perfect sense when you think about it. The beauty of these equations is that they let you predict how gases behave under different conditions.
Pro Tip Remember that temperature must always be in Kelvin for these equations to work!
For problems involving changing conditions, use (P₁V₁)/T₁ = (P₂V₂)/T₂ - this saves loads of time in calculations.
Root mean square (RMS) speed might sound complicated, but it's just a way of finding the average speed of gas particles that takes into account the fact that they're all moving at different speeds. You square all the individual speeds, find the mean, then take the square root.
The key equation here is P = (1/3)ρc̄², which connects pressure to the mean square speed of particles. This shows how molecular motion directly creates the pressure you can measure with instruments.
Here's the really cool bit the mean kinetic energy of gas particles is (3/2)kT per molecule. This means temperature is literally a measure of how fast particles are moving on average - higher temperature equals faster particles.
Mind-blowing fact Every gas particle at the same temperature has the same average kinetic energy, regardless of the gas type!
For a whole sample, the total kinetic energy becomes (3/2)nRT, linking molecular motion directly to measurable properties like temperature and pressure.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Explore the mechanisms of particle interactions through exchange particles and Feynman diagrams. This summary covers key concepts such as beta decay, fundamental forces, and the role of bosons in particle physics, essential for exam preparation.
PhysicsExplore detailed notes covering essential A-Level Physics concepts, including stellar luminosity, electromagnetic radiation, nuclear decay, and gas laws. This resource is designed for AQA and other exam boards, featuring interactive flashcard-style navigation for effective revision. Access the full notes here: https://www.notion.so/Physics-Revision-AQA-A-Level-a87264d9f28c4302b.
PhysicsComprehensive revision notes on Thermal Physics, including key concepts such as phase changes, specific latent heat, the ideal gas law, and the first law of thermodynamics. Ideal for AQA A Level Physics students preparing for exams, with practice questions included to enhance understanding.
PhysicsExplore key concepts in nuclear physics, including alpha decay, gamma radiation, and the structure of the nucleus. This summary provides essential information on radioactive emissions, their properties, and implications for safety. Ideal for AQA A Level Physics revision.
PhysicsExplore essential Feynman Diagrams for AQA A Level Physics, covering proton-proton collisions, electron interactions, and beta decay processes. This summary provides a clear understanding of subatomic particle interactions and nuclear equations, crucial for mastering Unit 2: Particles and Radiation.
PhysicsExplore the fundamental concepts of particle physics, including the structure of atoms, the classification of subatomic particles (hadrons, leptons, baryons, and mesons), and the significance of isotopes. This summary provides essential equations for calculating specific charge and examples of various particles, making it a valuable resource for A-Level physics students.
PhysicsApp Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Ever wondered why a gas heats up when you pump up a bike tyre, or why absolute zero is the coldest possible temperature? This topic explores the fascinating world of gases at the molecular level, covering everything from internal energy... Show more
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Think of internal energy as the total energy stored inside any object - it's basically all the kinetic and potential energy of every single particle added together. The kinetic energy comes from particles buzzing about randomly (especially noticeable in gases), whilst potential energy comes from how these particles interact with each other.
What's brilliant about internal energy is that it depends entirely on the state of your object. Change the temperature, pressure, or volume, and you'll change the internal energy too. Here's the key bit: adding heat to a system always increases its energy, but that doesn't necessarily mean the temperature goes up every time.
For ideal gases, life gets much simpler because we assume the particles don't interact with each other. This means they only have kinetic energy, no potential energy to worry about.
Quick Tip: Remember that internal energy is about the total energy of all particles - not just the average!
The internal energy of an ideal gas follows the equation U = (3/2)nRT, where n is the number of moles, R is the gas constant, and T is temperature in Kelvin.
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Improve your grades
Join milions of students
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Specific heat capacity tells you how stubborn a material is about changing temperature - it's the energy needed to warm up 1kg of something by just 1K. Water's particularly awkward with a massive specific heat capacity of 4180 J/kg·K, which is why it takes ages to boil a kettle!
The equation Q = mcΔθ is your best friend here. Q is the heat energy, m is mass, c is specific heat capacity, and Δθ is the temperature change. Pretty straightforward once you get the hang of it.
Latent heat is completely different - this is energy that goes into changing state (like melting or boiling) rather than changing temperature. You've got latent heat of fusion (solid to liquid), vaporisation (liquid to gas), and sublimation (solid straight to gas).
The Kelvin scale starts at absolute zero where particles theoretically stop moving completely. The brilliant thing is that 1K = 1°C in terms of temperature differences, so conversions are dead easy.
Remember: At absolute zero, gas particles have no kinetic energy and exert zero pressure!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The kinetic theory makes some clever assumptions about ideal gases that make the maths work beautifully. Particles are tiny compared to their container, they only interact during perfectly elastic collisions, and they're constantly moving in random directions.
This leads to the classic gas laws you need to know: pressure is proportional to temperature , pressure is inversely proportional to volume (Boyle's law), and volume is proportional to temperature (Charles' law). These all combine into the relationship PV/T = constant.
Pressure in gases comes from particles smashing into container walls and changing momentum. When a particle hits a wall, it experiences a momentum change of 2mv (since it bounces back). This constant bombardment creates the steady pressure you can measure.
Key Insight: Gas pressure is literally millions of tiny molecular collisions happening every second!
The rate of momentum change gives you force, and force per unit area gives you pressure - it's that simple.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
A mole is just Avogadro's number (6.02 × 10²³) of particles - think of it as chemistry's way of counting ridiculously large numbers. One mole of any substance has a mass in grams equal to its relative atomic or molecular mass.
The ideal gas equation comes in two handy forms: PV = nRT (using moles) or PV = NkT (using actual particle numbers). R is the molar gas constant and k is Boltzmann's constant .
These constants are related by R = kN_A, which makes perfect sense when you think about it. The beauty of these equations is that they let you predict how gases behave under different conditions.
Pro Tip: Remember that temperature must always be in Kelvin for these equations to work!
For problems involving changing conditions, use (P₁V₁)/T₁ = (P₂V₂)/T₂ - this saves loads of time in calculations.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Root mean square (RMS) speed might sound complicated, but it's just a way of finding the average speed of gas particles that takes into account the fact that they're all moving at different speeds. You square all the individual speeds, find the mean, then take the square root.
The key equation here is P = (1/3)ρc̄², which connects pressure to the mean square speed of particles. This shows how molecular motion directly creates the pressure you can measure with instruments.
Here's the really cool bit: the mean kinetic energy of gas particles is (3/2)kT per molecule. This means temperature is literally a measure of how fast particles are moving on average - higher temperature equals faster particles.
Mind-blowing fact: Every gas particle at the same temperature has the same average kinetic energy, regardless of the gas type!
For a whole sample, the total kinetic energy becomes (3/2)nRT, linking molecular motion directly to measurable properties like temperature and pressure.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
9
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the mechanisms of particle interactions through exchange particles and Feynman diagrams. This summary covers key concepts such as beta decay, fundamental forces, and the role of bosons in particle physics, essential for exam preparation.
PhysicsExplore detailed notes covering essential A-Level Physics concepts, including stellar luminosity, electromagnetic radiation, nuclear decay, and gas laws. This resource is designed for AQA and other exam boards, featuring interactive flashcard-style navigation for effective revision. Access the full notes here: https://www.notion.so/Physics-Revision-AQA-A-Level-a87264d9f28c4302b.
PhysicsComprehensive revision notes on Thermal Physics, including key concepts such as phase changes, specific latent heat, the ideal gas law, and the first law of thermodynamics. Ideal for AQA A Level Physics students preparing for exams, with practice questions included to enhance understanding.
PhysicsExplore key concepts in nuclear physics, including alpha decay, gamma radiation, and the structure of the nucleus. This summary provides essential information on radioactive emissions, their properties, and implications for safety. Ideal for AQA A Level Physics revision.
PhysicsExplore essential Feynman Diagrams for AQA A Level Physics, covering proton-proton collisions, electron interactions, and beta decay processes. This summary provides a clear understanding of subatomic particle interactions and nuclear equations, crucial for mastering Unit 2: Particles and Radiation.
PhysicsExplore the fundamental concepts of particle physics, including the structure of atoms, the classification of subatomic particles (hadrons, leptons, baryons, and mesons), and the significance of isotopes. This summary provides essential equations for calculating specific charge and examples of various particles, making it a valuable resource for A-Level physics students.
PhysicsApp Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Sociology