A gas is contained in a vertical piston-cylinder assembly by a piston with a face area of 40 in2 and weight of 100 lbf. The atmosphere exerts a pressure of 14.7 lbf/in2 on top of the piston. A paddlewheel transfers 3 Btu of energy to the gas during a process in which the elevation of the piston increases slowly by 2 ft. The piston and cylinder are poor thermal conductors, and friction between the piston and cylinder can be neglected. Determine the work done by the gas on the piston, in Btu, and the change in internal energy of the gas, in Btu.

.8834 btu

Explanation:

Given  

Area of the piston  = 40

The weight W = 100 Ibf

Atmospheric pressure  = 14.7 Ibf/

Work added E = 3 Btu

The change in the elevation ah = +2 ft —> 2 x 12 = 24 in  

Required

The change in internal energy of the gas ΔU in Btu

Assumption

The piston and cylinder are poor thermal conductors.

Friction can be neglected.

solution:

for piston

ΔPE=║W+(*A)║*Δh

ΔPE=8256 lbf.in

      =8256*.000107

      =.8834 btu

from the first law of conversation of energy then, the changing in the potential energy of the piston is made by exerting force by the gas:

-ΔPE

       = --.8834 btu

for the gas as a system, and by applying first law of thermodynamics

Q-W=Δ-->0-(--.8834)

     =.8834 btu