Question

In an isothermal change, an ideal gas obeys
A. Boyle’s Law
B. Charle’s Law
C. Gay-Lussac Law
D. None of these

Answer 1

Hint:
In an Isothermal process in a thermodynamic system, the temperature is constant and at a constant temperature, the effect on the other parameters such as pressure, volume, work-done, heat energy, etc., varies with the given conditions of the system and surroundings and can be stated in various form of laws of ideal gas that are given in options.


Formula used:
An Ideal-Gas Equation, $PV = nRT$


Complete step by step solution:

An isothermal Process in thermodynamics is defined as the process during which the temperature $T$ of a system remains constant that’s why it is also referred to as a constant-temperature process.
In an Isothermal process, $\,Change{\text{ }}in{\text{ }}Temperature = \Delta T = 0$ i.e., $T = constant$
We know that an ideal-gas equation can be stated as: -
$PV = nRT$
In an Isothermal change, $T = constant$
$ \Rightarrow PV = nR(constant)$
As $n\,and\,R$ are constant for given ideal gas.
$ \Rightarrow PV = constant$
Also, we know that at a constant temperature, the change in volume of a gas is inversely proportional to the pressure exerted by it (according to Boyles Law).
i.e., $PV = constant\,(say\,k)$
Thus, in an isothermal change, an ideal gas obeys “Boyle’s Law”.
Hence, the correct option is (A) Boyle’s Law.




Note:
 In this problem, to determine which law of an ideal gas obeys an isothermal change, use $\Delta T = 0$ and hence, analyze each and every given option carefully to give a precise explanation by simplifying ideal gas equation with respect to isothermal change and provide the exact reasons in support of your explanation.