Question

Using the expression dS=(CP/T)dT−VαdPdS=(CP/T)dT−VαdP, calculate the decrease in temperature that occurs if 1.10 moles of water at 298 K and 1085 bar are brought to a final pressure of 1.00 bar in a reversible adiabatic process. Assume that κT=0κT=0. Density of water is 0.998 g⋅cm−3g⋅cm−3, α=2.04×10−4K−1α=2.04×10−4K−1, CP=75.3J⋅K−1⋅mol−1CP=75.3J⋅K−1⋅mol−1.

Answer 1

Adiabatic system defines as the system where the change of heat does not take place. Thus dq = 0 .

We know that for a reversible process the the change in entropy is defined as  ds = dq/T . Where T is the temperature in Kelvin scale.

Thus for the reversible adiabatic process, ds = 0 .

The final temperature of the system is 293 K.

So, the temperature of the system decreases by 5 K to that of initial value.

The detail calculation is shown below.