Question

The pressure and temperature of $4d{m^3}$ carbon dioxide gas are doubled. Then volume of carbon dioxide would be:
A: $2d{m^3}$
B: $3d{m^3}$
C: $4d{m^3}$
D: $8d{m^3}$

Answer 1

There is an equation called the ideal gas equation. This equation relates pressure, volume, temperature and number of moles of gas with each other. With the help of this equation we can solve any problem related to temperature, volume and pressure of gas.

Formula used: $\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
Where ${P_1},{V_1},{T_1}$ is initial pressure, temperature and volume of gas and ${P_2},{V_2},{T_2}$ is final pressure, temperature and volume of gas.

Complete step by step answer:
In this question the initial pressure and temperature of gas is doubled and we have to find the final volume of the gas. This can be found by using the ideal gas equation. This equation relates pressure, volume, temperature and number of moles of gas with each other. According to this equation,
$PV = nRT$
Where, $P$ is pressure, $V$ is volume, $n$ is number of moles, $R$ is gas constant and $T$ is temperature.
In this question we have changed the pressure and temperature of gas, and we have to find the effect on volume on changing these quantities. Therefore the number of moles and gas constant will remain the same before and after making the change. So, equation can be written as,
$\dfrac{{PV}}{T} = {\text{constant}}$
This means,
$\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$ (Ratio before making changes is equal to ratio after making changes)
According to the question, ${P_2} = 2{P_1}$ and ${T_2} = 2{T_1}$. Substituting these values in the equation,
$\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{2{P_1}{V_2}}}{{2{T_1}}}$
Solving this we get,
${V_1} = {V_2}$
This means the initial volume is equal to the final volume. Initial volume is $4d{m^3}$ (given) therefore final volume is also equal to $4d{m^3}$ (solved above).
So, the correct answer is option C.

Note:
Ideal gas equation is derived by taking some assumptions. Some of these assumptions are, the gas consists of a very large number of particles, which obey Newton's laws and are in random motion. Volume of the molecules is very small as compared to the volume occupied by the gas.