Question

An ideal monatomic gas is contained within a cylinder by a moveable piston. The gas is in thermal contact with a heat bath initially at 310 K. What is the change in molar entropy if the gas is heated to 600 K if:

A. The piston is blocked

B. The piston is allowed to move freely against atmospheric pressure

Answer 1

Let degree of freedom of the gas be denoted by f.

Let T₁ be initial Temperature and T₂ be the final temperature.

Then change in entropy(ΔS)

1.At constant volume

ΔS=n*Cv(lnT2/T1)

where n=no. of moles.

C_v=(f* R)/2 R is gas constant

2.At constant Pressure

ΔS=n * Cp * ln(T2/T1)

where C_p=((f+2)*R)/2

Referring to the question above.Since it is momoatomic gas therefore f=3 and also I am assuming number of moles of gas be 1.

Also R=8.314 J

Now consider the Case A.

It is the case for constant Volume.Therefore

ΔS=(1*(3*8.314)*ln(600/310))/2 =8.24 J

Similarly for Case B

T₁=310 K

T₂=600K

C_p=(f+2)*R/2=20.78

Therefore

ΔS=1*20.78*ln(600/310)=13.72 J