Chapter 15, Problem 14STP

Interpretation Introduction

Interpretation:

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

Concept introduction:

When pressure and amount of gas are kept constant, increasing the temperature of gas increases its volume. This law is known as Charles’ Law.

According to this law,

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Where

${\mathrm{T}}_1$ is initial temperature of the gas

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

${\mathrm{T}}_2$ is the final temperature of the gas

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

Answer to Problem 14STP

The new temperature of the gas should be $771.4K$

Explanation of Solution

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

If ${\mathrm{V}}_1$ is the volume of the gas at temperature ${\mathrm{T}}_1$ and temperature is changed to ${\mathrm{T}}_2$ then volume is changed to ${\mathrm{V}}_2$. The formula used to calculate ${\mathrm{V}}_2$ is

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Or

${\mathrm{T}}_2=\frac{V_2{T}_1}{V_1}$

Given data is:

${\text{V}}_1=2.1L$

$T_1=300K$

${\mathrm{V}}_2=5.4L$

On substituting the values in the formula:

$\begin{array}{c}{T}_2=\frac{5.4\times 300}{2.1}\\ =771.4K\end{array}$

Therefore temperature is $771.4K$

Conclusion

The gas must be heated to the temperature of $771.4K$.