Answer:
.8834 btu
Explanation:
Given
Area of the piston [tex]A_{piston}[/tex]= 40 [tex]in^{2}[/tex]
The weight W = 100 Ibf
Atmospheric pressure [tex]P_{atm}[/tex]= 14.7 Ibf/ [tex]in^{2}[/tex]
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+([tex]P_{atm}[/tex]*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:
[tex]W_{gas}=[/tex]-ΔPE
= --.8834 btu
for the gas as a system, and by applying first law of thermodynamics
Q-W=Δ[tex]U_{gas}[/tex]-->0-(--.8834)
=.8834 btu
