[bu2012]

A vessel containing 2.25mol of an ideal gas with Pi = 1.00 bar and Cp,m = 5R/2 is in thermal contact with a water bath. Treat the vessel gas, and water bath as being in thermal equilibrium, initially at 312K, and as separated by adiabatic walls from the rest of the universe. The vessel, gas, and water bath have an average heat capacity of Cp = 6250. J/K. The gas is compressed reversibly to Pf = 10.5 bar. What is the temperature of the system after thermal equilibrium has been established?

[bu2012]

Well I believe first I need to do an adiabatic reversible compression on the gas in the cylinder. But I'm not sure what equation to use that deals with pressures. I have mainly used V2/V1 = (T1/T2)^Cv/R. Am I missing out on an equation?

[bu2012]

I just realized that that equation if for expansion, not compression. However, I'm not sure what equation the compression one is?

[saden99]

Hmmm...perhaps instead of thinking of it as compression think of it as non-expansion.

Some of the question is meant to simplify any equations you use.

[jusy1]

Hi everyone,

bu2012, the equation for adiabatic reversible expansion or compression will be the same:

T_f/T_i = (V_i/V_f)^{Cp/Cv - 1}

To use pressure instead of volume, use the ideal gas law: p_iV_i/p_fV_f = T_i/T_f

so you get T_f/T_i = (p_f/p_i)^(a-1)/a where a = Cp/Cv (you know that Cp - Cv = nR).

Knowing that W = C_v * (T_f-T_i): W = RT_i/(a-1) * [(p_f/p_i)^(a-1)/a -1]

To solve the problem you can consider your system as including the vessel ,the gas and the water in thermal contact. Then, knowing the work that has been performed on the adiabatic system, you can get the final temperature (you may assume your system's C_p = C_v).