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There are a couple of questions on my practice exam I am stuck on. If you could point me in the right direction I'd appreciate it.

1. A gas is described by the equation PV= RT+aT^2 where a is some gas specific constant. Find (dU/dV)@constant T

And provide an expression for the isothermal reversible work

I think I was able to solve for the work as it is just the integral of pdV which is easy enough to compute. If this is incorrect could someone please tell me.

2. The minimum amount of work to cool a refrigerator from 300K to 200K if the heat capacity of the refrigerator is 1000J/K. The exterior is assumed to be at a constant 300K despite being used as a heat sink.

The hint for this one says to think of it as a carnot engine in reverse but I don't know what this means exactly. I found the efficiency of this if it were a Carnot engine and it is 1/3 then I just assumed minimum work was the product of the efficiency heat capactiy and temperature difference (300-200) . I suspect however that this is wrong.

3. Lastly, the heat capacity of some monatomic ideal gas is Cv=2.5R and Cp=3.5R, what is the heat capacity of a process where P/V is a constant i.e. the ratio of P:V is constant. I gathered that if P/V is constant, as PV=nRT then the process is isothermal and that perhaps the Cp/v is infinite, as dU for an isothermal process is 0.

1. A gas is described by the equation PV= RT+aT^2 where a is some gas specific constant. Find (dU/dV)@constant T

And provide an expression for the isothermal reversible work

I think I was able to solve for the work as it is just the integral of pdV which is easy enough to compute. If this is incorrect could someone please tell me.

2. The minimum amount of work to cool a refrigerator from 300K to 200K if the heat capacity of the refrigerator is 1000J/K. The exterior is assumed to be at a constant 300K despite being used as a heat sink.

The hint for this one says to think of it as a carnot engine in reverse but I don't know what this means exactly. I found the efficiency of this if it were a Carnot engine and it is 1/3 then I just assumed minimum work was the product of the efficiency heat capactiy and temperature difference (300-200) . I suspect however that this is wrong.

3. Lastly, the heat capacity of some monatomic ideal gas is Cv=2.5R and Cp=3.5R, what is the heat capacity of a process where P/V is a constant i.e. the ratio of P:V is constant. I gathered that if P/V is constant, as PV=nRT then the process is isothermal and that perhaps the Cp/v is infinite, as dU for an isothermal process is 0.

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