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 answer:

p₂ =  1.92 MPa

Step-by-step explanation:

$$\begin{gathered} t_1=27°C\to K=27+273.16K=300.16K \\ {p}_1=4\text{MPa} \\ {t}_2=15°C\to K=15+273.16K=288.16K \\ {V}_2=2\cdot V_1 \\ \frac{pV}{T}=konst \\ \frac{p_1\cdot V_1}{t_1}=\frac{p_2\cdot V_2}{t_2} \\ \frac{p_1\cdot V_1}{t_1}=\frac{p_2\cdot 2V_1}{t_2} \\ \frac{p_1}{t_1}=\frac{p_2\cdot 2}{t_2} \\ {p}_2=\frac{t_2}{2\cdot t_1}\cdot p_1=\frac{288.16}{2\cdot 300.16}\cdot 4=\frac{1801}{938}\text{MPa}=1.92\text{MPa} \end{gathered}$$

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