The PV diagram in the figure below shows a set of thermodynamic processes that m

Question

The PV diagram in the figure below shows a set of thermodynamic processes that make up a cycle ABCDA for a monatomic gas, where AB is an isothermal expansion occurring at a temperature of 390 K. There are 2.05 mol of gas undergoing the cycle with

PA = 1.01 106 Pa,

PB = 4.80 105 Pa,

and

PC = 2.02 105 Pa.

(a) Find the volumes VA and VB.

(b) Find the work done in each process of the cycle and the total work done for the whole cycle.

(c) Find the change in thermal energy during the constant-volume process BC.
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Explanation / Answer

a) use, PA*VA = n*R*T

==> VA = n*R*T/PA

= 2.05*8.314*390/(1.01*10^6)

= 0.00658 m^3

simillarly, VB = n*R*T/PB

= 2.05*8.314*390/(4.8*10^5)

= 0.0138 m^3

b) W_AB = n*R*T*ln(VB/VA)

= 2.05*8.314*390*ln(0.0138/0.00658)

= 4923 J

W_BC = 0

W_CD = -PC(VB - VA)

= -2.02*10^5*(0.0138 - 0.00658)

= -1458 J

WDA = 0

W_total = W_AB + W_BC + W_CD + W_DA

= 4923 + 0 - 1458 + 0

= 3465 J

c)

change in thermal energy = 0

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