Biology
Chemistry
AP Chemistry
English
AP English Literature
Physics
Dec 5, 2025
70
3 pages
Elizabeth Gabante @elizabethgabante_mpdt
Thermal physics deals with the relationship between heat, temperature, and energy in systems. Understanding these concepts helps explain... Show more
When two objects reach the same temperature with no heat transferring between them, they've achieved thermal equilibrium. This stable state means temperature and pressure are uniform throughout both systems.
Temperature measures the average kinetic energy of particles, while heat is energy transferred between bodies due to temperature differences. Remember that thermal contact doesn't require physical touching—objects just need to be close enough to exchange energy. The Zeroth Law tells us that if objects A and B are each in thermal equilibrium with object C, then A and B are also in equilibrium with each other.
Materials typically expand when heated and contract when cooled. For linear expansion, we use , where α is the coefficient of linear expansion. Area expansion follows where $\gamma = 2\alpha$, and volume expansion follows where $\beta = 3\alpha$.
Pro Tip When converting between temperature scales, remember that Celsius to Kelvin just requires adding 273, while Fahrenheit to Celsius uses .
Thermal expansion has important real-world applications that require precise calculations. When materials heat up, both containers and their contents expand, but often at different rates.
In the example of gasoline in an aluminum container, we need to account for both materials expanding. Gasoline expands significantly more than aluminum with coefficients of $9.6 \times 10^{-4}/°C$ and $24 \times 10^{-6}/°C$ respectively. When calculating spills, we find the difference between the expansion of the liquid and the container.
Different materials expand at different rates. Metals like aluminum and lead have higher expansion coefficients than glass, which is why glass containers sometimes crack when hot liquids are poured into them. Liquids generally expand more than solids, with gasoline and turpentine having particularly high expansion rates.
Remember When solving thermal expansion problems, always account for the expansion of both the container and its contents—failing to do so will give incorrect results!
An ideal gas is a theoretical model of randomly moving molecules that helps us understand gas behavior. The ideal gas law, , connects pressure (P), volume (V), number of moles (n), temperature (T), and the universal gas constant .
Several related laws describe specific gas behaviors Charles' law says volume increases with temperature, Gay-Lussac's law states pressure increases with temperature, and Avogadro's law says volume increases with the number of moles. Boyle's law shows the inverse relationship between pressure and volume—as one goes up, the other goes down.
The kinetic theory of gases helps explain these behaviors at the molecular level. The root mean square (rms) speed of gas molecules is given by , where is Boltzmann's constant. The average kinetic energy per molecule is .
Quick Check The internal energy of an ideal gas depends only on temperature, not pressure or volume, and can be calculated as for n moles of gas.
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
3
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
notes on the cases on different mirror ray diagrams
Physicsnotes on lens ray diagrams and their cases
PhysicsMaster the art of drawing ray diagrams for convex and concave lenses. This guide covers essential concepts like real and virtual images, focal points, and step-by-step instructions for accurate diagram creation. Ideal for physics students seeking clarity in optics.
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Elizabeth Gabante
@elizabethgabante_mpdt
Thermal physics deals with the relationship between heat, temperature, and energy in systems. Understanding these concepts helps explain everyday phenomena like why materials expand when heated and how gases behave under different conditions.
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
When two objects reach the same temperature with no heat transferring between them, they've achieved thermal equilibrium. This stable state means temperature and pressure are uniform throughout both systems.
Temperature measures the average kinetic energy of particles, while heat is energy transferred between bodies due to temperature differences. Remember that thermal contact doesn't require physical touching—objects just need to be close enough to exchange energy. The Zeroth Law tells us that if objects A and B are each in thermal equilibrium with object C, then A and B are also in equilibrium with each other.
Materials typically expand when heated and contract when cooled. For linear expansion, we use , where α is the coefficient of linear expansion. Area expansion follows where $\gamma = 2\alpha$, and volume expansion follows where $\beta = 3\alpha$.
Pro Tip: When converting between temperature scales, remember that Celsius to Kelvin just requires adding 273, while Fahrenheit to Celsius uses .
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Thermal expansion has important real-world applications that require precise calculations. When materials heat up, both containers and their contents expand, but often at different rates.
In the example of gasoline in an aluminum container, we need to account for both materials expanding. Gasoline expands significantly more than aluminum with coefficients of $9.6 \times 10^{-4}/°C$ and $24 \times 10^{-6}/°C$ respectively. When calculating spills, we find the difference between the expansion of the liquid and the container.
Different materials expand at different rates. Metals like aluminum and lead have higher expansion coefficients than glass, which is why glass containers sometimes crack when hot liquids are poured into them. Liquids generally expand more than solids, with gasoline and turpentine having particularly high expansion rates.
Remember: When solving thermal expansion problems, always account for the expansion of both the container and its contents—failing to do so will give incorrect results!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
An ideal gas is a theoretical model of randomly moving molecules that helps us understand gas behavior. The ideal gas law, , connects pressure (P), volume (V), number of moles (n), temperature (T), and the universal gas constant .
Several related laws describe specific gas behaviors: Charles' law says volume increases with temperature, Gay-Lussac's law states pressure increases with temperature, and Avogadro's law says volume increases with the number of moles. Boyle's law shows the inverse relationship between pressure and volume—as one goes up, the other goes down.
The kinetic theory of gases helps explain these behaviors at the molecular level. The root mean square (rms) speed of gas molecules is given by , where is Boltzmann's constant. The average kinetic energy per molecule is .
Quick Check: The internal energy of an ideal gas depends only on temperature, not pressure or volume, and can be calculated as for n moles of gas.
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
3
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
notes on the cases on different mirror ray diagrams
Physicsnotes on lens ray diagrams and their cases
PhysicsMaster the art of drawing ray diagrams for convex and concave lenses. This guide covers essential concepts like real and virtual images, focal points, and step-by-step instructions for accurate diagram creation. Ideal for physics students seeking clarity in optics.
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
