Chapter 15, Problem 65GP

To determine

The heat required for the process.

Answer to Problem 65GP

The heat required for the process is $200\text{J}$ .

Explanation of Solution

Given info:

The cross sectional area of the jar is, $A=0.080{\text{m}}^2$ .

The mass of the piston is, $m=0.10\text{kg}$ .

The rise of the piston is, $h=1\text{cm}=0.01\text{m}$ .

The outside pressure is, $P=1\times {10}^5\text{N}/{\text{m}}^2$ .

Formula Used:

The expression to calculate the internal energy of the gas is,

  $\Delta U=\frac{3}{2}PV$

The expression to calculate the volume of the gas is,

  $V=Ah$

The expression to calculate the heat required for process is,

  $\begin{array}{l}Q=\Delta U+PV\\ Q=\frac{3}{2}PV+PV\\ Q=\frac{5}{2}PAh\end{array}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}Q=\frac{5}{2}\left(1\times {10}^5\text{N}/{\text{m}}^2\right)\left(0.080{\text{m}}^2\right)\left(0.01\text{m}\right)\\ =200\text{J}\end{array}$

Conclusion:

Thus, the heat required for the process is $200\text{J}$ .