At point D in the figure below, the pressure and temperature of 2.00 mol of an i

Question

At point D in the figure below, the pressure and temperature of 2.00 mol of an ideal monatomic gas are 2.00 atm and 360 K, respectively. The volume of the gas at point B on the PV diagram is three times that at point D and its pressure is twice that at point C. Paths AB and CD represent isothermal processes. The gas is carried through a complete cycle along the path DABCD. Determine the total amount of work done by the gas and the heat absorbed by the gas along each portion of the cycle.

Wby gas,tot=__________kJ

QDA=_________kJ

QAB=_________kJ

QBC=________kJ

Wby gas,tot=__________kJ

QDA=_________kJ

QAB=_________kJ

QBC=________kJ

Explanation / Answer

VD = n R TD / PD

= 2 X 8.314 X 360 / 2 X 101.3 = 29.5 L

VB = VC = 3VD = 88.5 L

PC =n R TC / VC

PC = 2 X 8.206 X 10-2 X 360 / 88.5

PC = 0.667 atm

PB = 2 PC

PB = 1.33 atm

TD = Tc = 360K

TA = TB = PB VB / n R

= 1.33 X 88.5 / 2 X 8.206 X 10-2

= 720K

PA = 2 PD = 4 atm

QD-->A = 3 / 2 n R dT

QD-->A = 3/2 X 2 X 8.314 X (720-360)

QD-->A = 8.98 kJ

QA-->B = nRT ln( VB / VA )

QA-->B = 2 X 8.314 X 720 X ln ( 88.5 / 29.5 )

QA-->B = 13.1 kJ

QB-->C = 1 / 2 nR(TC-TB )

QB-->C = 1 /2 X 2 X 8.314 X (360-720)

QB-->C = -8.98kJ

QC-->D =n RTln(VD/VC)

QC-->D = 2 X 8.314 X 360 X ln(29.5/88.5)

QC-->D = -6.58 kJ

By adding the total value Wtotal = 6.62 kJ

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