A system is designed that permits continuous programmed control of the pressure

Question

A system is designed that permits continuous programmed control of the pressure and volume of the gas that it contains. The system is filled with one mole of helium and brought to an initial condition of one atmosphere and 8 liters. It is then reversibly compressed to 2 liters along a programmed path given by the relationship; v=-2p^2 +10

where P is in atmospheres and V is in liters. Assume that the helium gas behaves as an ideal gas.

(a) What is the final temperature(K) of the system?

? 236.4 ? 42.5 ? 48.7 ? 53.1 ? 58.3

(b) What is the heat absorbed by the system in l·atm/mol?

? -8.3 ? -10.8 ? -12.3 ? -15.3 ? -17.8

(c) The work done by the system in J/mol?

? -945.6 ? -376.2 ? 376.2 ? 945.6 ? None of above

Explanation / Answer

a) Since the moles of helium are constant, n is constant ,so in the ideal gas equation,PV=NRT

V=-2P2 + 10, putting value of V as 2l, P=2atm,N=1

T=PV/NR=2(2)/1(0.082)=48.7K

Final temperature is 48.7K

Similarly, for the initial temperature, T=PV/NR=1(8)/1(0.082)=97.56K

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