Question

Two moles of a gas at 1 bar and 298 K are compressed at constant temperature by use of a constant pressure of 5 bar. How much work is done on the gas ? If the compression is driven by a 100-kg mass, how far will it fall in the earth's gravitational field ? ($g=9.8m{s}^{-2}$)

Answer 1

W = -P $\Delta$ V
= -$\Delta$ PV = - $\Delta$ nRT
$w=-P_2(V_2-V_1)=-P_2(\frac{nRT}{P_2}-\frac{nRT}{P_1})$
$w=-nRT(1-\frac{P_2}{P_1})$
$=-2\times 8.314\times 298(1-\frac{5}{1})=+19820J$
$w=hmg$
h = $\frac{w}{mg}=\frac{19820}{110\times 9.8}=20.22m$