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 paddle wheel transfers 3 Btu of energy to the gas during a process in which the elevation of the piston increases by 1 ft. The piston and cylinder are poor thermal conductors, and friction between them can be neglected. Determine the change in internal energy of the gas, in Btu.

ΔU=0.8834 Btu

Explanation:

Given data

Area of piston A=40 in²

The weight W=100 lbf

Atmospheric Pressure P=14.7 lbf/in²

Work added E=3 Btu

The change in elevation Δh=1 ft =12 inch

To find

Change in internal energy of the gas ΔU

Solution

For Piston

ΔPE=| W+(P×A)×Δh |

ΔPE=| 100+(14.7×40)×12 |

ΔPE=8256 lbf.in

ΔPE=8256×0.000107

ΔPE=0.8834 Btu

From law of conservation of energy then ,the charging in the potential energy of the piston is made by exerting force by gas

Wgas= -ΔPE

Wgas= -0.8834 Btu

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

Q-W=ΔU

0-(-0.8834 Btu)=ΔU

So

ΔU=0.8834 Btu