# Thermal Physics - Calculating Work, Heat, and Internal Energy in a Gas Cylinder

• Niles
In summary, the conversation is about a cylinder containing one litre of air at a given temperature and pressure. A massless piston is pushed in suddenly with a force of 2000 N, causing the piston to move 1 mm before being stopped. The questions asked are about the work done on the system, the amount of heat added to the gas, the increase in internal energy, and the change in entropy of the gas once it returns to equilibrium. The work done is positive, no heat is added, and the internal energy is equal to the work done. The change in entropy can be calculated using the Ideal Gas Properties of Air table.
Niles

## Homework Statement

A cylinder contains one litre of air at T = 300 K and P = 105
Pa. At one end of the cylinder is a massless piston, whose
surface area is 0.01 m^2. Suppose you push the piston in
suddenly, with a force of 2000 N. The piston moves only 1
mm, before being stopped by an immovable barrier.
(a) How much work have you done on the system?

(b) How much heat has been added to the gas?

(c) Assuming that all the energy added goes to the gas,
how much does the internal energy of the gas increase?

(d) Use the thermodynamic identity (dU = T dS −
PdV ) to calculate the change in entropy of the gas
(once it is back in equilibrium).

## The Attempt at a Solution

a) The work done is simply: W = F*d - and the work done is positive.

b) No heat is being added, right? So the internal energy is just equal the work done one the gas, and the temperature rises. Can you confirm this statement?

c) We have (considering that b is correct) that dU = W.

d) Here I am a little lost. Can I calculate the entropy when dU = 0 and then when dU != 0 and then add them?

Last edited:
Check the Ideal Gas Properties of Air table in any thermodynamic text. That should point you in the right direction.

## 1. What is thermal physics and what does it study?

Thermal physics is the branch of physics that deals with the relationship between heat and energy. It studies the behavior and properties of matter at the atomic and molecular level in relation to temperature and thermal energy.

## 2. What is the difference between heat and temperature?

Heat is the transfer of thermal energy from one object to another, while temperature is a measure of the average kinetic energy of the particles in a substance. Heat is measured in joules, while temperature is measured in degrees Celsius or Kelvin.

## 3. How does heat transfer occur?

Heat can transfer through three main methods: conduction, convection, and radiation. Conduction is the transfer of heat through direct contact between two objects, convection is the transfer of heat through the movement of fluids, and radiation is the transfer of heat through electromagnetic waves.

## 4. What is the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. This means that the total energy in a closed system remains constant.

## 5. How does thermal expansion work?

Thermal expansion is the increase in size or volume of a substance when its temperature increases. This occurs because the particles in the substance gain kinetic energy and move more, causing the substance to expand. Different substances have different rates of thermal expansion.

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