Answer to Question #249440 in Mechanical Engineering for russman

Question

A quantity of gas has an initial pressure and volume of 0.1 MN/m² and 0.1 m³. respectively. It is compressed to a final pressure of 1.4 MN/m² according to the law PV^1.26= constant. Determine the final volume of the gas.

Answer 1

$$PV^{1.26}=\text{constant}$$

$$\dfrac{V_2}{V_1}=(\dfrac{P_1}{P_2})^{1/1.26}$$

$$V_2=V_1(\dfrac{P_1}{P_2})^{1/1.26}$$

$$V_2=0.1 m^3\bigg(\dfrac{0.1 MN/m^2}{1.4 MN/m^2}\bigg)^{1/1.26}\approx0.0123\ m^3$$

The final volume of the gas is $0.0123$ m³.^.