Question

If a given mass of a gas occupies a volume of 10cc at 1 atmospheric pressure and a temperature of ${{100}^{\circ }}C$ (373.15K). What will be its volume at 4 atmospheric pressure, the temperature being the same.
a)100cc
b)400cc
c)2.5cc
d)104cc

Answer 1

In the question it is given that the temperature of the gas remains constant. Therefore it can be implied that it is an isothermal process. Hence using the ideal gas equation we can determine the change in pressure as a result of change in volume at constant temperature.
Formula used:
$PV=nRT$

Complete answer:
Let us say we have a gas contained in a container. The gas in the container can be characterized by the thermodynamic variables that are temperature, pressure and volume. More precisely all the thermodynamic variables are related by a gas equation that is,
$PV=nRT$
Where ‘n’ is the number of moles or the amount of the gas and ‘R’ is a gas constant. Let us say a gas has pressure ${{P}_{1}}$ and volume ${{V}_{1}}$ on the PV diagram. Let us say we take another coordinate on the diagram such that for pressure equal to ${{P}_{2}}$ the volume occupied by the gas is ${{V}_{2}}$ . Now if the process is taking place at constant temperature, then using the ideal gas equation we can write,
${{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}=nRT...(1)$
Now using equation 1, the volume occupied by the gas at 4 atmospheric pressure is
$\begin{aligned} & {{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}} \\\ & \Rightarrow 1atm\times 10cc=4atm\times {{V}_{2}} \\\ & \Rightarrow {{V}_{2}}=2.5cc \\\ \end{aligned}$

Therefore the correct answer of the above question is option c.

Note:
The ideal gas equation is not always valid as in nature we don’t have a mixture of gasses. Also not all the gasses obey the gas equation at all temperatures and pressure. Therefore we need to introduce the correction factor based on the molecular theory for a gas and then accordingly proceed if mentioned in the question.