# Work done by a gas

## Homework Statement

A cylinder with a frictionless piston is placed horizontaly in an atmosphere of pressure 1.0×10^5N/m^2.A gas in the cylinder is initially at a temperature of 300K with a volume of 1.0 ×10^-3 m3.Then , the ags is heated slowly to a final temparature of 400k.How much work is done by the gas in this process?

PV=nRT
E=3/2nRT

## The Attempt at a Solution

I used this approach though I very much think there is a better approach
PV=nRT ,which everything given(before the gas was heated) I calculated n.
using E=3/2nRT I got the Energy before and after the difference and got the difference which I assume is equal to the work done

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TSny
Homework Helper
Gold Member
Hello.

To clarify the question: Is the gas heated "at 400 K" or is it heated "until the gas reaches a final temperature of 400 K"?

Also, you write E = (3/2)nRT. That is valid for a monatomic ideal gas. Does the problem state that the gas is monatomic? [EDIT: I don't think you'll actually need this equation anyway. The change in E does not equal the work because there is also some heat added to the gas.]

Hello.

To clarify the question: Is the gas heated "at 400 K" or is it heated "until the gas reaches a final temperature of 400 K"?

Also, you write E = (3/2)nRT. That is valid for a monatomic ideal gas. Does the problem state that the gas is monatomic? [EDIT: I don't think you'll actually need this equation anyway. The change in E does not equal the work because there is also some heat added to the gas.]
I have edited the question.
It is not stated that the gas is monoatomic and that is one of the things that make me think that my method is wrong.
My argument is the energy gained by the gas is equal to the difference in internal energy of the gas before heating and after heating.

TSny
Homework Helper
Gold Member
I think it will help if you sketch the process on a PV diagram. How can you get the work done by the gas from the PV diagram?

I think it will help if you sketch the process on a PV diagram. How can you get the work done by the gas from the PV diagram?
I think that the PV graph in this case should be a straight line parallel to the x-axis since the pressure is constant but the volume is varying(since the piston is moving).
I am not sure about this but since the pressure is constant I think this is an isobaric process and the work done can be got by multiplying the difference in volume(between final volume and initial volume) by the pressure(I can get this by using Boyle's Law)

TSny
Homework Helper
Gold Member
I think that the PV graph in this case should be a straight line parallel to the x-axis since the pressure is constant but the volume is varying(since the piston is moving).
I am not sure about this but since the pressure is constant I think this is an isobaric process and the work done can be got by multiplying the difference in volume(between final volume and initial volume) by the pressure(I can get this by using Boyle's Law)
Yes, that's very good (although it's not really Boyle's law that you are using). The important thing is that you have deduced that W = PΔV for this process. Can you now use the ideal gas law to rewrite PΔV in terms of ΔT?

Yes, that's very good (although it's not really Boyle's law that you are using). The important thing is that you have deduced that W = PΔV for this process. Can you now use the ideal gas law to rewrite PΔV in terms of ΔT?
Yes I am using ideal gas law,..my mistake.
I got it thanks