Thermodynamics - Compression Work

[eprparadox]

Hey guys and girls,

I wouldn't consider this a homework problem because I'm not in school. I'm just starting to prepare for next aprils GRE exam and so I was reading some thermo stuff from Daniel Schroeder's Introduction to Thermal Physics.

I'm working on a problem from his book that reads:
"Imagine some helium in a cylinder with an initial volume of 1 liter and an initial pressure of 1 atm. Somehow the helium is made to expand to a final volume of 3 liters, in such a way that its pressure rises in direct proportion to its volume."

(So the final pressure will be 3 atm if the final volume is 3 L)

so the first part of the question asks to compute the work done on the gas during the process so I just did the integral of Pdv from 1 L to 3 L and I got -4 J.

But then the next part asks for the change in the helium's energy content during this process. I don't know how to do this without finding the heat added to the system and sure enough the following part asks to find the amount of heat added to or removed from the helium during the process.

I think this is a simple problem and I'm just being dumb, but if anyone can point me in the right direction on how to find the head added that would be great.

And this is my first post so if I happen to be in the wrong area, please let me know. Thanks for all the help.

 

[jbsteele]

The energy change of a system is given by the equation ΔU = q + w, where U is the internal energy, q is heat and w is work. In this case, we know the work done on the gas is -4 J, so the energy change can be calculated by subtracting 4 J from the amount of heat added to or removed from the system. To find the amount of heat, you can use the equation q = ΔU + w. Solving for q, you can find the amount of heat added to or removed from the system.

 

[thomate1]

Hi there,

First off, great job on solving the first part of the problem by calculating the work done on the gas. To find the change in the helium's energy content, you can use the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. So in this case, the change in energy would be equal to the heat added, since there is no other work being done on the system.

To find the heat added, you can use the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature. Since the pressure and volume are changing in this process, you can use the initial and final values to calculate the change in energy.

Hope this helps and good luck on your GRE preparations!