Question

A cylinder of gas is compressed by a piston from an initial volume of 125 liters to a final volume of 90 liters. The compression occurs at constant pressure, and the work done on the gas by the piston is 104 joules. What is the gas pressure during the compression?
(1 liter = 10-3 meters3)

Answer 1

Task. A cylinder of gas is compressed by a piston from an initial volume of $V_{0}=125$ liters to a final volume of $V_{1}=90$ liters. The compression occurs at constant pressure $p$, and the work done on the gas by the piston is $A=104$ joules. What is the gas pressure during the compression? ($1$ liter $=10^{-3}$ meters^{3})

Solution. The work done for the compression of gas from volume $V_{0}$ to volume $V_{1}$ undeer constant pressure $p$ is given by the formula:

$A=p(V_{0}-V_{1}),$

whence

$p=\frac{A}{V_{0}-V_{1}}.$

Substituting values we obtain

$p=\frac{A}{V_{0}-V_{1}}=\frac{104}{(125-90)*10^{-3}}=\frac{104*10^{3}}{35}=2971.4\ \mathrm{Pa}.$

Answer. $p=2971.4\ \mathrm{Pa}.$