A rigid insulated tank consists of two compartments separated by a membrane. One

Question

A rigid insulated tank consists of two compartments separated by a membrane. One compartment, V = 5 ft3, contains air at 100 psia and 100degreeF. The second compartment, V = 10 ft3, is evacuated. The membrane ruptures and the air expands to fill the entire tank. Considering the air to be the thermodynamic system, determine (10 points, 2 points each) Work done (Btu) Heat transfer (Btu) The change in internal energy (Btu) The temperature (degree F) at the end of the process The pressure (psia) at the end of the process

Explanation / Answer

a) Since the second compartment is evacuated the resistance to gas from first compartment to exapnd to second compartment is zero. Hence, the work done is zero.

b) the tank is insulated so the heat transfer to or from the system is zero.

c)The 1st Law tells us that ?U = 0 when no work or heat transfer occur during a process on a closed system.

d) Also, because U is a function of T only for an ideal gas, T2 = T1.=100 0F

e) P1*V1 =P2*V2

P2=(V1/V2)*P1 = (V1/3*V1)*100 psia

= 100/3 = 33.33 psia

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