Three moles of an ideal gas are taken around the cycle a b c shown in the figure

Question

Three moles of an ideal gas are taken around the cycle abc shown in the figure (Figure 1) . For this gas, Cp=29.1 J/(molK). Process ac is at constant pressure, process ba is at constant volume, and process cb is adiabatic. The temperatures of the gas in states a, c, and b are Ta=300K, Tc= 492 K, and Tb= 600 K.

Part A

Calculate the total work W for the cycle.

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Figure 1 of 1

Three moles of an ideal gas are taken around the cycle abc shown in the figure (Figure 1) . For this gas, Cp=29.1 J/(molK). Process ac is at constant pressure, process ba is at constant volume, and process cb is adiabatic. The temperatures of the gas in states a, c, and b are Ta=300K, Tc= 492 K, and Tb= 600 K.

Part A

Calculate the total work W for the cycle.

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Figure 1 of 1

Explanation / Answer

given

n = 3

Cp = 29.1

so, cV = cP - R

= 29.1 - 8.314

= 20.786 J/(mol K)

gamma = Cp/Cv

= 29.1/20.786

= 1.4

so, the given gas in diatomic.

we know, workdone in adiabatic process,

Wcb = n*R*(Tb - Tc)/(1 - gamma)

= 3*8.314*(600 - 492)/(1 - 1.4)

= -6734 J

here negative sign indicaates, work is done on the gas.

Workdone in expanding the gas,

Wac = Pa*(VC - VA)

= n*R*(Tc-TA)

= 3*8.314*(492 - 300)

= +4788 J

Wba = 0

so, net workdone, Wnet = Wac + Wcb + Wba

= 4788 - 6734 + 0

= -1946 J <<<<<<<<<--------------------Answer

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