## Related questions with answers

Nitrogen at $900\ \mathrm{kPa}$ and $300^{\circ} \mathrm{C}$ is expanded adiabatically in a closed system to $100\ \mathrm{kPa}$. Find the minimum nitrogen temperature after the expansion.

Solution

VerifiedNitrogen is an ideal gas. To obtain the final temperature when nitrogen is expanded isentropically we will use the isentropic relation of an ideal gas under constant specific heat assumption.

$\frac{T_{2}}{T_1}=\left(\frac{P_{2}}{P_{1}}\right)^{(k-1) / k}$

Since we don't know the final temperature yet, we will assume that the average temperature is $450$ K. The specific heat ratio of nitrogen can be found in Table A-2b to be $k=1.391$. Thus the final temperature is:

$\begin{aligned} T_{2} &=& T_{1}\left(\frac{P_{2}}{P_{1}}\right)^{(k-1) / k}\\ &=& (300+273 \mathrm{~K})\left(\frac{100 \mathrm{kPa}}{900 \mathrm{kPa}}\right)^{0.391 / 1.391}\\ &=& \boxed{309 \mathrm{~K}} \end{aligned}$

The actual average air temperature is $441$ K, therefore our assumed average temperature of 450 K is good enough.

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