Question

Carbon dioxide (CO2) gas within a piston–cylinder assembly undergoes a process from a state where p1 = 5 lbf/in.2 , V1 = 2.5 ft3 to a state where p2 = 20 lbf/in.2 , V2 = 0.5 ft3 . The relationship between pressure and volume during the process is given by p = 23.75 − 7.5V, where V is in ft3 and p is in lbf/in.2 . Determine the work for the process, in Btu.

Answer 1

Answer:

work 24.31 ft³/in²

Explanation:

The work in thermodynamic processes is given by a relationship between pressure changes and volume differences as follows:

W = - $\int\limits^{V2}_{V1} {p} \, dV$

In this exercise they give the pressure ratio P = 23.75 -7.5 V, so we can evaluate the integral between points two V1 = 2.5 ft3 and V2 = 0.5 ft3

W = - [23.75 V -7.5 V² / 2]

W = - [23.75 (0.5 -2.5) - 7.5 (0.5² - 2.5²) / 2]

W = - [-47.5 + 23.19] BTU

W = 24.31 ft3 / in2 = 24.31 BTU

Note that the work is positive since work is done on the gas to compress it.