A horizontal rigid cylinder is well-insulated and divided into two compartments

Question

A horizontal rigid cylinder is well-insulated and divided into two compartments by a piston that is free to move, but does not let the gases leak into the other compartment. Initially on one side there is 1 m3 of N2 gas at 500 kPa and 120 oC. The other side contains 1 m3 of He gas at 500 kPa and 40 oC. Heat transfers through the piston and thermal equilibrium is established between the two parts. Using constant specific heats at room temperature, find the final equilibrium temperature, in oC. Answer: 85.6 oC

Explanation / Answer

Area of one side,A1=1 m3 of N2 gas

Pressure,P1=500 kPa

Temperature,T1=20oC.

Area of the other side,A2=1 m3 of He gas

Pressure,P2= 500 kPa

Temperature,T2=40 oC.

Let us assume that both the Helium and Nitrogen are ideal gases with constant specific heats

Energy stored in container is negligible

Cylinder is well insulated

Gas constants and volume specific heats are for nitrogen and helium are respectively,

R=0.2968 kPa.m3/kg.K

Cv=0.743KJ/Kg.C

R=2.07 kPa.m3/kg.K

Cv=3.1156 KJ/Kg.C

We know that Ein-Eout=Total E of the system

That is net energy transfer is the change in internal, kinetic and potential energies etc

So, 0=dU=dU,N2-dU,He

0=(mcv(T2-T1))N2-(mcv(T2-T1))He

Substituting we get,

0=(4.287)(0.743)(Tf-120)+(0.7691)(3.1156)(Tf-40)

So Tf=85.60C

Tf is the final equilibrium temperature of the system

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