Question

A gas in a piston–cylinder assembly undergoes a process for which the relationship between pressure and volume is pV2 5 constant. The initial pressure is 1 bar, the initial volume is 0.1 m3, and the final pressure is 9 bar. Determine (a) the final volume, in m3, and (b) the work for the process, in kJ.

Answer 1

Answer:

Part a)

$V_2 = 0.033 m^3$

Part b)

$W = -20 kJ$

Explanation:

Part a)

As we know that the gas equation is given as

$PV^2 = constant$

so here we know that

$P_1 = 1 bar$

$P_2 = 9 bar$

$V_1 = 0.1 m^3$

Now in order to find the final volume we have

$V_2^2 = \frac{P_1V_1^2}{P_2}$

$V_2^2 = \frac{1 \times 0.1^2}{9}$

$V_2 = 0.033 m^3$

Part b)

Work done in this process is given as

$W = \int P dV$

$W = \int \frac{k}{V^2} dV$

$W = \int_{0.1}^{0.033} \frac{k}{V^2} dV$

$W = -\frac{k}{V_2} + \frac{k}{V_1}$

$W = - \frac{P_2V_2^2}{V_2} + \frac{P_1V_1^2}{V_1}$

$W = P_1V_1 - P_2V_2$

$W = (1\times 10^5)(0.1) - (9 \times 10^5)(0.033)$

$W = -20 kJ$