Question

When the pressure of 5L of $N_2$ is double and its temperature is raised from 300K to 600K, the final volume of the gas would be:
A. 10 L
B. 5 L
C. 15 L
D. 20 L

Answer 1

Hint: The combination of Boyle’s law, Charle’s law and Gay-Lussac’s law is known as the combined gas law. It is used for denoting the relationship between the volume of the gas, pressure of the gas and its absolute temperature for the fixed amount of the gas. The ideal gas law will be obtained if Avogadro's law is added in the combined gas law.

Formula used: As per combined gas law,
$\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
${P_1}$ is the initial pressure and ${P_2}$ is the final pressure of nitrogen gas.
${V_1}$ is the initial volume and ${V_2}$ is the final volume of nitrogen gas.
${T_1}$ is the initial temperature and ${T_2}$ is the final temperature of nitrogen gas.

Complete step by step answer:
Let us first note down the values given in the question.
${T_1} = 300K$ and ${T_2} = 600K$
${V_1} = 5L$
The value initial volume is given, but we have to find out the final volume of ${N_2}$ gas.
The value of initial pressure of ${N_2}$ is not given, so let us assume it as $x$.
The final pressure of ${N_2}$ will be twice as that of initial pressure of ${N_2}$. It will be $2x$.
As per combined gas law,
$\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
Let us substitute the respective values in the above formula to calculate the final volume of ${N_2}$ gas.
$\dfrac{{x \times 5}}{{300}} = \dfrac{{2x \times {V_2}}}{{600}}$
$\therefore 5x = \dfrac{{2x \times {V_2} \times 300}}{{600}}$
$\therefore 5x = \dfrac{{2x \times {V_2}}}{2}$
$\therefore 5x \times 2 = 2x \times {V_2}$
$\therefore 10x = 2x \times {V_2}$
$\therefore {V_2} = \dfrac{{10x}}{{2x}}$
$\therefore {V_2} = 5L$
The final volume of ${N_2}$ gas is 5L.

So, the correct answer is Option B.

Additional information:
The combined gas law is less accurate at high temperature and pressure.
The combined gas law has real life applications. It is used in the field of thermodynamics and fluid mechanics. The law is also used for calculation of pressure, volume or temperature of the gas in clouds and these calculated values are used in weather forecasting.

Note: According to the combined gas law, the ratio of products of pressure and volume of the gas to the absolute temperature of that gas is a constant.
Hence, the combined gas law can be expressed as:
$\dfrac{{PV}}{T} = k$
Here, $k$ is a constant only when the amount of gas is constant.