Question

The following sets of values for ${{C}_{V}}$ and ${{C}_{P}}$ of an ideal gas have been reported by different students. The units are cal/mol.K . Which of these sets is most reliable?
(A) ${{C}_{V}}$=3, ${{C}_{P}}$=5
(B) ${{C}_{V}}$=4, ${{C}_{P}}$=5
(C) ${{C}_{V}}$=3, ${{C}_{P}}$=5
(D) ${{C}_{V}}$=3, ${{C}_{P}}$=4.2

Answer 1

Hint: The molar heat capacity of any substance is defined as the amount of heat energy required to change the temperature of 1 mole of that substance by 1 unit. It depends on the nature, size, and composition of the system.

Complete answer:
The molar heat capacity C, at constant pressure, is represented ${{C}_{P}}$ by .
At constant volume, the molar heat capacity C is represented ${{C}_{V}}$ by .
Value of ${{C}_{P}}$ and ${{C}_{V}}$ for monatomic gas is $\dfrac{5}{2}R$ and $\dfrac{3}{2}R$ respectively.
Since in the question unit are terms of calories, therefore, the value of R,universal gas constant will be equal to 2 cal. Therefore, putting the value of R in the value of molar heat capacities we get, ${{C}_{P}}$=5 and ${{C}_{V}}$=3.

Hence the correct answer is A option.

Note:
When heat is absorbed by a body, the temperature of the body increases. And when heat is lost, the temperature decreases. The temperature of an object is the measure of the total kinetic energy of the particles that make up that object. So when heat is absorbed by an object this heat gets translated into the kinetic energy of the particles and as a result the temperature increases. Thus, the change in temperature is proportional to the heat transfer.