Calculating Work in Ideal Gas Systems with Movable Pistons

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To calculate the work done on an ideal gas in a cylinder with a movable piston as its temperature increases from T1 to T2, the ideal gas law (PV = nRT) can be used to express pressure in terms of volume. The work done is defined as W = -∫PdV, where pressure can be derived from the force exerted by the piston (P = F/A). The discussion raises questions about whether the work is done on the gas or by the gas, clarifying that it is indeed the work done on the gas. The relationship between the number of moles, mass, and molar mass is also noted as n = m/M. Understanding these principles is crucial for accurately calculating the work in this scenario.
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Homework Statement



An ideal gas is enclosed in a cylinder that has a movable piston on top. The piston has a mass m and an area A and is free to slide up and down, keeping the pressure of the gas constant. How much work is done on the gas as the temperature of n mol of the gas is raised from T1 to T2? (Use T_1 for T1, T_2 for T2, and m, A, R, and n as necessary.)

Homework Equations


n=m/M
P=F/A
PV=nRT
PV=(kB)T
W=- integral of P dV from Vf to Vi ( sorry I was not sure how to format this!)

The Attempt at a Solution


I was not sure how to go about doing this. Do I set the ideal gas law equal to volume and then plug that into work?
 
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Is this work done on the gas or by the gas?
 
It's the work that is done on the gas I believe.
 

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