Question

# An ideal monatomic gas is contained within a cylinder by a moveable piston. The gas is...

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

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.

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

2.At constant Pressure

ΔS=n * Cp * ln(T2/T1)

where Cp=((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

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

Therefore

ΔS=1*20.78*ln(600/310)=13.72 J

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