Question

Work is done by a substance in a reversible nonflow manner in accordance with v = (700/p) m³, where p is in kPaa. Evaluate the work done on or by the substance as the pressure increases from 70 kPaa to 700 kPaa. 

W = kJ

Answer in 2 Decimals

Answer 1

Solution;

$V=(\frac{700}{P})m^3$

Differentiate;

$dV=\frac{-700}{P^2}dP$

Work is calculated as;

$W=\int PdV$

$W=\int P(\frac{-700}{P^2})dP$

$W=-700\int\frac1PdP$

$W=-700[ln(P)]_{70}^{700}$

$W=-700[ln(700)-ln(70)]$

$W=-1611.809565kJ$

Answer;

W=-1611.81kJ