Chapter 13, Problem 59A

To determine

New volume of the gas in cylinder.

Answer to Problem 59A

  $0.14m^3$

Explanation of Solution

Given:

Area of piston, $A=0.015m^2$

Volume of cylinder, $V_1=0.23m^3$

Initial pressure of gas, $P_1=1.5\times {10}^{5}Pa$

Amount of mass placed on piston, $m=150kg$

Temperature is constant.

Formula used:

From Boyle’s Law:

  $P_1{V}_1=P_2{V}_2$

Thus,

  $\begin{array}{l}{V}_2=\frac{P_1{V}_1}{P_2}\\ V_2=\frac{P_1{V}_1}{\left(P_1+\frac{mg}{A}\right)}\end{array}$

Calculation: Volume of container after putting $150kg$ mass on it is:

  $V_2=\frac{(1.5\times {10}^{5}Pa)(0.23m^3)}{1.5\times {10}^{5}Pa+\frac{(150kg)(9.8\text{}N/kg)}{0.015m^2}}$

  $V_2=0.14m^3$

Conclusion: Hence, volume of cylinder after 150 kg mass is put on it is $0.14m^3$ .