Compressed gas

The pressure vessel contains a compressed gas at a temperature t1 = 27°C and a pressure p1 = 4 MPa. How much does its pressure change when we release half the amount of gas and its temperature drops to t2 = 15°C?

Correct result:

p₂ =  1.1111 MPa

Solution:

$$\begin{gathered} t_1=27^{\circ }\text{C } \\ {p}_1=4\text{ MPa } \\ {t}_2=15^{\circ }\text{C } \\ {V}_2=2\cdot V_1 \\ {\displaystyle \frac{pV}{T}}=konst \\ {\displaystyle \frac{p_1\cdot V_1}{t_1}}={\displaystyle \frac{p_2\cdot V_2}{t_2}} \\ {\displaystyle \frac{p_1\cdot V_1}{t_1}}={\displaystyle \frac{p_2\cdot 2V_1}{t_2}} \\ {\displaystyle \frac{p_1}{t_1}}={\displaystyle \frac{p_2\cdot 2}{t_2}} \\ {p}_2={\displaystyle \frac{t_2}{2\cdot t_1}}\cdot p_1={\displaystyle \frac{15}{2\cdot 27}}\cdot 4={\displaystyle \frac{10}{9}}=1.1111\text{ MPa} \end{gathered}$$

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