Chapter 13, Problem 96A

Interpretation Introduction

Interpretation:

The pressure of the gas is to be calculated for a given new volume when the temperature and amount of gas are constant.

Concept introduction:

When temperature and amount of gas are constant, pressure of gas is inversely proportional to the volume of the gas. This law is known as Boyle’s Law.

According to this law,

${\mathrm{P}}_1{V}_1=P_2{V}_2$

Where

${\mathrm{P}}_1$ is initial pressure of the gas

${\mathrm{V}}_1$ is initial volume of the gas

${\mathrm{P}}_2$ is the final pressure of the gas

${\mathrm{V}}_2$ is the final volume of the gas

Answer to Problem 96A

The new pressure of the gas is $1.17atm$.

Explanation of Solution

The change in volume on changing the pressure of the gas keeping the temperature fixed is studied by a law named as Boyle’s Law. According to this law, Product of pressure and volume of a given mass of gas is constant at constant temperature.

If ${\mathrm{V}}_1$ is the volume of the gas at pressure ${\mathrm{P}}_1$ and volume is increased to ${\mathrm{V}}_2$ Then pressure is decreased to ${\mathrm{P}}_2$. The formula used to calculate ${\mathrm{P}}_2$ is

${\mathrm{P}}_1{V}_1=P_2{V}_2$

Or

${\mathrm{P}}_2=\frac{P_1{V}_1}{V_2}$

Given data is:

$\begin{array}{l}{\text{V}}_1\text{=1L}\\ {\text{P}}_1\text{=3}\text{.50}\text{atm}\\ {\text{V}}_2=1+2\\ =3L\end{array}$

On substituting the values in the formula:

$\begin{array}{c}{P}_2=\frac{1\times 3.50}{\begin{array}{l}3\end{array}}\\ =1.17atm\end{array}$

Therefore new pressure is $1.17atm$.

Conclusion

The pressure of the gas on opening the valve is $1.17atm$.