Question

Volume of a gas become four times if

(A) Temperature become four times at constant pressure
(B) Temperature becomes one fourth at constant pressure
(C) Temperature becomes two times at constant pressure
(D) Temperature becomes half at constant pressure

Answer 1

Hint: Here the volume of a gas is increased to four times of its initial value and the increase in temperature of the gas is asked in the question. For this first you need to know the ideal gas law to know about how the volume and temperature of a gas is related to each other at constant pressure.

Formula used:
The ideal gas equation is given by;
$PV = nRT$
Where, P is the pressure of the gas
V is the volume of the gas
n is the amount of substance
R is the universal gas constant
T is the temperature of the gas


Complete answer:
We know that:
The ideal gas law, also known as the general gas equation, is the state equation of a hypothetical ideal gas. It is a good assumption of the behaviour of many gases under many conditions.
The ideal gas equation is given by;
$PV = nRT$

At constant pressure, we know that;
$\dfrac{{nR}}{P} = \dfrac{V}{T}$ is constant
So, $\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{{T_2}}}$
$\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{4{V_1}}}{{{T_2}}}$
Therefore, when the volume is increased by four times then temperature has to be increased by 4 times too at constant pressure.
${T_2} = 4{T_1}$

Hence the correct answer is Option(A).



Note: We can directly use Charle’s Law which states a directly proportional relationship between volume and temperature at constant pressure. Also, keep in mind that temperature should be used in Kelvin if the question is of numerical type.