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 polytropic exponent.

• A. $1.81$
• B. $9.19$
• C. $1.9$
• D. $9.1$

Answer 1

The correct option is A $1.81$

In polytropic process:

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

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

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

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

$\eta \left(0.4911\right)=(\eta -1)\left(1.098\right)$

$\therefore \eta =1.81$