# Calculating Internal Energy Change in a Gas Under Constant Pressure

• duds1234
In summary, a gas is compressed at a constant pressure of 0.639 atm from 5.41 L to 2.3 L, with 470 J of energy leaving the gas by heat. The work done on the gas is 201.3057131J. There appears to be an error in the question statement as it states that 470 J of energy leaves the gas, but in the calculation for part b, the value 407 J is used. Assuming that 470 J is the correct value, the change in internal energy of the gas is -268.6942869J.
duds1234
Hello, this is my first post, so I apologize in advance if it's not quite up to par.

## Homework Statement

A gas is compressed at a constant pressure of 0.639 atm from 5.41 L to 2.3 L. In the process, 470 J of energy leaves the gas by heat.
a) What is the work done on the gas (J)?
b) What is the change in its internal energy(J)?

a) ##W=-PΔV##
b) ##ΔU=Q+W##

## The Attempt at a Solution

a)
##P = 0.639atm {\frac{1Pa}{9.872*10^-6atm}} = 64728.52512Pa##
##ΔV = V_f - V_i = 2.3L - 5.41L = -3.11L {\frac{1*10^{-3}m^3}{1L}} = -0.00311m^3##
##W = -P ΔV = -6.4728.52512Pa * -0.00311m^3 = 201.3057131J##

I submitted my answer to part a and it was correct. Part b is what I need help with. I believe that I am doing it correctly, but my answer is returned as incorrect. My incorrect work and answer appears below.

b)
##ΔU = Q + W = -407J + 201.3057131J = -205.6942869J##

Any insight into why my work/answer for part b is incorrect would be greatly appreciated!

If your answer to part a is correct, then I can't see what's wrong with your answer to part b (see EDIT)

Is this a multi choice question that is automatically assessed?

EDIT: Just noticed that in the question statement you say that 470J of energy leaves, but in the calculation for part b you use the figure 407J

Last edited:
Unfortunately, this isn't a multiple choice question. I have to submit my answers electronically and a computer grades them. I have confirmation that part a is correct and that my answer for b is incorrect.

Ok. Can you confirm which value of heat leaving the gas is correct: 407 J or 470 J

1 person
It is 470, thus this would be my error in part b. Thank you very much for helping me find my silly mistake. The correct answer would be -268.6942869J.

You're welcome. It happens to everyone now and then!

## 1. What is internal energy?

Internal energy is the total energy stored within a system, including the kinetic and potential energies of its particles. It is a measure of the microscopic components of a system and their interactions with each other.

## 2. How does internal energy change?

Internal energy can change through processes such as heating or cooling, chemical reactions, or work done on or by the system. These processes can result in a transfer of energy into or out of the system, causing a change in its internal energy.

## 3. What factors affect the change in internal energy?

The change in internal energy of a system depends on the amount of heat transferred, the work done, and the change in the system's temperature and composition. Other factors, such as pressure and volume, may also play a role in certain processes.

## 4. What is the relationship between change in internal energy and temperature?

The change in internal energy is directly proportional to the change in temperature, as described by the equation ΔU = nCΔT, where ΔU is the change in internal energy, n is the number of moles of substance, and C is the specific heat capacity of the substance.

## 5. How is change in internal energy measured?

The change in internal energy can be measured using calorimetry, which involves measuring the heat transferred between the system and its surroundings. This can also be calculated by using the known values of heat transferred, work done, and temperature change in the system.

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