Question

A piston/cylinder contains water at ${500}^{o}C,3MPa$. It is cooled in a polytropic process to ${200}^{o}C,1MPa$. Find the specific work in the process.

• A. $2155kJ$
• B. $3089kJ$
• C. $1255kJ$
• D. $5152kJ$

Answer 1

The correct option is B $3089kJ$

In polytropic process:

$\frac{T^{\eta }}{P^{\eta -1}}=constant$

$\therefore (\frac{500+273}{200+273}{)}^{\eta }=(\frac{3}{1}{)}^{\eta -1}$

$(\frac{773}{473}{)}^{\eta }=\frac{1}{3}$

$\eta \ln \left(\frac{773}{473\times 3}\right)=\ln \left(\frac{1}{3}\right)$

$\therefore \eta =\frac{-1.18}{-.607}=1.81$

Work done:
$W=\frac{R\Delta T}{\eta -1}=\frac{8.34\times 300}{1.81-1}=3089J$