Question 668: Thermodynamics & KTG

Question

How much should the pressure be increased in order to reduce the volume of a given mass of gas by $5 \%$ at the constant temperature?

Accepted Answer

At constant temperature,
$$ P_1 V_1=P_2 V_2 \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)$$
Volume $\left(\mathrm{V}_1ight)$ is decreased by $5 \%$
$$ \begin{array}{ll} 	herefore & \mathrm{V}_2=\mathrm{V}_1-\mathrm{V}_1\left(\frac{5}{100}ight) \ & \frac{\mathrm{V}_2}{\mathrm{~V}_1}=\left(1-\frac{5}{100}ight)=\frac{19}{20} \ 	herefore & \frac{\mathrm{P}_1}{\mathrm{P}_2}=\frac{19}{20} \end{array} $$
Increase in pressure,
$$ \begin{array}{ll} 	herefore & P_2-P_1=\frac{20}{19} P_1-P_1 \ 	herefore & P_2-P_1=P_1 \frac{1}{19}=P_1 	imes 0.0526 \end{array} $$
i.e. pressure should be increased by $5.26 \%$ of $\mathrm{P}_1$

Answer

$5 \%$

Answer

$10 \%$

Answer

$5.26 \%$

Answer

$4 \%$

Thermodynamics & KTG

How much should the pressure be increased in order to reduce the volume of a given mass of gas by 5 \% at the constant temperature?

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