A 4.00 L sample of a diatomic ideal gas with specific heat ratio1.40, confined t

Question

A 4.00 L sample of a diatomic ideal gas with specific heat ratio1.40, confined to a cylinder, is carried through a closed cycle.The gas is initially at 1.00 atm and at 300 K. First, its pressureis tripled under constant volume. Then, it expands adiabatically toits original pressure. Finally, the gas is compressed isobaricallyto its original volume.

(a) Determine the volume of the gas at the end of the adiabaticexpansion.

(b) Find the temperature of the gas at the start of the adiabaticexpansion.

(c) Find the temperature at the end of the cycle.

(d) What was the net work done on the gas for this cycle?

Explanation / Answer

(b)for an adiabatic expansion P * V^ = constant P1 * V1^ = P2 * V2^ or V2 = (P1/P2)^(1/) * V1 here,P2 = 3P1, = 1.40 for an ideal diatomic gas and V1 =1.00 atm = 1.00 * 1.013 * 10^5 Pa (c)the temperature of the gas at the start of the adiabaticexpansion (P1 * V1/T1) = (P2 * V2/T2) or T2 = (P2 * V2) * (T1/P1 * V1) ------------(1) T1 = 300 K (d)the volume of the gas when it expands adiabatically to itsoriginal pressure P2 * V2^ = P3 * V3^ or V3 = (P2/P1)^(1/) * V2 ------------(2) when the gas is compressed isobarically to its originalvolume (P2 * V2/T2) = (P3 * V3/T3) or T3 = (P3 * V3) * (T2/P2 * V2) here,P2 = P3 or T3 = (V3/V2) * T2 ------------(3) from (1) and (2) T3 = [(P2/P1)^(1/) * V2/V2] * T2 = (P2/P1)^(1/) *T2 P2 = 3P1 and T2 is given by equation (1) (e)the net work done on the gas for this cycle
W = P1 * V1^ + P2 * V2^

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