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Purple Baron
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Homework Statement
Derive an expression for the change in internal energy of 1 mol of an ideal gas for expansion from volume [itex] V_i [/itex] to [itex]V_f [/itex] under constant pressure of 1atm where [itex] \gamma = \frac{C_p}{C_v}=\frac{5}{3} [/itex]
Homework Equations
[itex] \Delta U=\frac{3}{2}nR\Delta T[/itex]
[itex]PV=nRT[/itex]
The Attempt at a Solution
My first idea is to find a way to get the change in temperature, I tried to do this by finding the initial temperature saying that: [itex]T_i=\frac{PV_i}{nR}[/itex] and finding the final temperature by substituting this into [itex]T_f=\frac{V_{i}^{\gamma - 1}}{V_{f}^{\gamma - 1}}T_i[/itex] and substituting the equation obtained for initial temperature. From this I found change in temperature and substituted into the change in internal energy equation did the algebra and obtained [itex]\Delta U=\frac{3}{2}PV_i((\frac{V_i}{V_f})^{\gamma - 1}-1)[/itex]; however I'm not sure about the answer as the question also says you may use the fact that for 1 mol of an ideal gas [itex]C_p-C_v=R[/itex] however nowhere did I need to use this, indeed, R canceled out of my final expression also th internal energy in my expression is dependent on the pressure, which I know is not the case, so I am unsure this is a valid approach. Thanks.
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