An ideal gas initially at pressure P 0 , volume V 0 , and temperature T 0 is tak

Question

An ideal gas initially at pressure P0, volume V0, and temperature T0 is taken through the cycle described in the figure below. (Assume n = 6 and m = 7.)

An ideal gas initially at pressure P0, volume V0, and temperature T0 is taken through the cycle described in the figure below. (Assume n = 6 and m = 7.) Find the net work done by the gas per cycle in terms of P0 and V0. What is the net energy Q added to the system per cycle? (Use any variable or symbol stated above as necessary.) Obtain a numerical value for the net work done per cycle for 1.00 mol of gas initially at 0 degree C. Recall that the work done by the system equals the area under a PV curve.

Explanation / Answer

a)
W = n*Po*(m*Vo - Vo)

= 6*Po(7*Vo-Vo)

= 36*Po*Vo

b)

dU = (3/2)*n*R*dT

= (3/2)*(Po*m*Vo - Po*Vo)

= (3/2)*6*po*vo

= 9*Po*Vo

dQ = dU + dW

= 9*po*vO + 36*Po*Vo

= 45*Po*Vo

c)

W = n*Po*(m*Vo - Vo)

= 6*Po(7*Vo-Vo)

= 36*Po*Vo

= 36*n*R*To

= 36*1*8.314*(273)

= 81710 J

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