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## Homework Statement

A fixed quantity of gas is originally at 20 atmospheres in a volume of 1 litre and a temperature of 300K suddenly expands and comes to equilibrium with a volume of 50 litres and a pressure of 1 atmosphere. If the process is irreversible and involves the transfer of heat and work derive an expression for the difference in the internal energy of the gas in Joules. Take:

[tex] C_{v} = \frac{5R}{2} mol^{-1} [/tex]

## Homework Equations

dU = dW + dQ

[tex] C_{v} = ( \frac{dQ}{dT} )_{V} [/tex]

The specification of Cv (even though the volume isn't constant in this problem) suggests using the state function:

U = U(T,V)

## The Attempt at a Solution

Prph! Where to start?!? First I calculated the final value of T using just the equation of state. I got me my partial differential for dU:

[tex] dU = ( \frac{dU}{dV} )_{T} dV + ( \frac{dU}{dT} )_{V} dT [/tex]

and... that's it. We've only ever been shown how to do reversible processes with one constant so I have no clue where to start with this. Any pointers would be much appreciated.

Cheers,

El Hombre

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