First slide

Different type of processes

Question

The gas inside a balloon has a pressure of 8 atmosphere at 27°C. It suddenly bursts. If for the gas $\frac{C_{p}}{C_{v}} = 1 .5$ ,find the resulting temperature.

Easy

A

27 K
B

-37° C
C

-123° C
D

150° C

Solution

The expansion process is adiabatic.
$\begin{array}{l} ∴ \frac{T_{2}}{T_{1}} = {(\frac{P_{2}}{P_{1}})}^{\frac{γ - 1}{γ}} \\ \Rightarrow \frac{T_{2}}{300} = {(\frac{1}{8})}^{\frac{1 .5 - 1}{1 .5}} = {(\frac{1}{8})}^{1 / 3} = 1 / 2 \\ T_{2} = 150 K \\ ∴ t_{2} = (150 - 273)^{\circ} C = - 123^{\circ} C . \end{array}$

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