A monatomic, ideal gas is in a sealed container (the number of gas molecules is

Question

A monatomic, ideal gas is in a sealed container (the number of gas molecules is always constant: n = 2 moles); the initial pressure is Pi = 1.01 x 105 Pa and the initial volume is Vi = 0.0224 m3.

First, the volume of the gas is decreased at a constant pressure (at Pi = 1.01 x 105 Pa) to a final volume of Vf = 0.0155 m3.

Second, the pressure of the gas is increased at a constant volume (at Vf = 0.0155 m3) to a final pressure of Pf = 1.35 x 105 Pa.

How much heat was added to (give as a positive number) or removed from (give as a negative number) the system? (The gas constant R = 8.31 J/mole-K.)

Explanation / Answer

At constant pressure, as volume is decreased,

H = nCp*(T2-T1)

Heat removed=2*5/2*R(T2-T1)

& from ideal gas law,

nR(T2-T1) = P(V2-V1) = 1*10^5* (0.0224-0.0155) =690 J

Heat removed = 5/2*n*R(T2-T1) = 1725 J

When volume is constant,

Heat added = Cv*n*(T2-T1) = 3/2* n*R*(T2-T1) = 3/2* V(P2-P1) = 3/2*0.0155*(0.34*10^5) =790.5 J

So net heat removed = 1725 -790.5 = -934.5 J (ANS)

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