Question

In a piston-cylinder arrangement, air with a volume of 0.1 m3 and a pressure of 100 kPa is compressed until pv2 = sbt until its pressure reaches 900 kPa. Find the volume of air in the final state and the work done during the process.

Answer 1

Solution;

Given ;

$pv^2=c$

$V_1=0.1m^3$

$P_1=100kPa$

$P_2=900kPa$

For final Temperature;

$P_1V_1^2=P_2V_2^2$

Hence;

$V_2=V_1(\frac{P_1}{P_2})^{\frac12}$

$V_2=0.1(\frac{100}{900})^{0.5}$

$V_2=0.0333m^3$

The work done during the process;

$W_{1-2}=\frac{P_2V_2-P_1V_1}{1-n}$

$W_{1-2}=\frac{(900×0.0333)-(100×0.1)}{1-2}$

$W_{1-2}=-19.7kJ$