Question

At constant volume, pressure is directly proportional to the temperature, this law popularly known as:
(A) Charles law
(B) Boyle's law
(C) Gay Lussac law
(D) Avagadros law

Answer 1

Hint: The gas law which contains terms like temperature (T), pressure (P), volume (V) gives a relation between them, which is PV=nRT. This is also known as the ideal gas law.

Complete step by step solution:
Before writing the answer for the above solution let’s understand each option in detail:
Charles law: according to this law the volume of an ideal gas changes with the change in the absolute temperature, when the pressure of the system is constant throughout the experiment. It is the ratio of volume of temperature where the pressure is always constant.
\[\dfrac{{{V}_{1}}}{{{T}_{1}}}=\dfrac{{{V}_{2}}}{{{T}_{2}}}\]
Pressure and number of moles are constant.
Boyle’s law: According to this law at the constant temperature, the pressure applied to an ideal gas is inversely proportional to the volume of the system. This means that the product of pressure and volume is constant.
\[{{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}\]
Temperature is constant.
Avagadros law: according to this law at constant pressure and absolute temperature, the number of moles is directly proportional to the volume of the gas. This means that the ratio of volume and number of moles is constant.
\[\dfrac{{{V}_{1}}}{{{n}_{1}}}=\dfrac{{{V}_{2}}}{{{n}_{2}}}\]
Gay Lussac law: according to this law the pressure of a given mass of gas varies directly with the absolute temperature of the gas when volume is kept constant.
\[P\alpha T\]

Hence, the correct answer is (C) gay Lussac law.

Note: If we combine Boyles and Charles law a new equation is formed:
\[\dfrac{{{P}_{1}}{{V}_{1}}}{{{T}_{1}}}=\dfrac{{{P}_{2}}{{V}_{2}}}{{{T}_{2}}}\]
In this equation pressure, volume and temperature all are variables and also the product of pressure and volume in the reaction changes proportionally with the absolute temperature.