Question

A 1.79 mol diatomic gas initially at 274 K undergoes this cycle: It is (1) heated at constant volume to 707 K, (2) then allowed to expand isothermally to its initial pressure, (3) then compressed at constant pressure to its initial state. Assuming the gas molecules neither rotate nor oscillate, find (a) the net energy transferred as heat to the gas (excluding energy transferred as heat out of the gas), (b) the net work done by the gas, and (c) the efficiency of the cycle.

Answer 1

a)

n = number of moles = 1.79

T1 = initial temperature = 274 K

T2 = final temperature = 707 K

At constant volume ,

Q1 = n cv (T2 - T1) = (1.79) (12.5) (707 - 274) = 9688.375 J

During isothermal process :

Q2 = n R T1 ln(T2/T1) = (1.79)(8.314) (274) ln(707/274) = 3865.25 J

At constant pressure :

Q3 = n cp (T1 - T2) = (1.79) (20.785) (274 - 707 ) = - 16109.83 J

Q = Q1 + Q2 = 9688.375 + 3865.25 = 13553.625 J

b)

W = Q + Q3 = 13553.625 + ( - 16109.83) = - 2556.21 J

c)

efficiency is given as

= W/Q = 2556.21 /13553.625 = 0.19