A vessel containing 1.60 mol of an ideal gas with Pi=2.50bar 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...

A vessel containing 1.60 mol of an ideal gas with Pi=2.50bar 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 312 K, and separated by adiabatic walls from the rest of the universe. The vessel, gas, and water bath have an average heat capacity of CP=2800.J⋅K−1. The gas is compressed reversibly to Pf=15.0bar.

What is the temperature of the system after thermal equilibrium has been established?