Question

In isothermal expansion, the pressure is determined by
A. Temperature only
B. Compressibility only
C. Temperature and compressibility both
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 and volume varies with the given conditions of the system and surroundings. Therefore, apply $PV = nRT$ to identify the correct option for the given problem.

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 Isothermal process, $\,Change{\text{ }}in{\text{ }}Temperature = \Delta T = 0$
i.e., $T = constant$
Now, 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 a given ideal gas.
$ \Rightarrow PV = constant$
$ \Rightarrow {P_1}{V_1} = {P_2}{V_2}$
It can also be written as: -
$ \Rightarrow {P_2} = {P_1}\dfrac{{{V_1}}}{{{V_2}}}$
which means ${P_2} < {P_1}$
As a result, the only variable depending on the system's volume or compressibility is the pressure.
Or in other words, the only variable, pressure, is dependent on compressibility only.
Thus, in isothermal expansion, the pressure is determined by Compressibility only.
Hence, the correct option is (B) Compressibility only.




Note:
In this problem, to determine pressure is dependent whether on temperature or compressibility we have to apply the condition of isothermal change, i.e., $\Delta T = 0$ in an ideal gas equation and simplify it and then analyze each given option carefully to give an accurate answer with exact reasons.