Question

Let Cv and Cp denote the molar heat capacities of an ideal gas at constant volume and constant pressure respectively. Which of the following is a universal constant?
(a) CpCv
(b) CpCv
(c) Cp − Cv
(d) Cp + Cv

Answer 1

For an ideal gas, Cp − Cv = R

Correct option is (C)

Explanation:

(c) Cp − Cv

• For an ideal gas, Cp − Cv = R
• Where Cv and Cp denote the molar heat capacities of an ideal gas at constant volume and constant pressure respectively.
• Here R is the gas constant whose value is 8.314 J/K.
• Therefore, Cp − Cv is a constant.
• On the other hand, the ratio of these two varies as the atomicity of the gas changes.
• Also, their sum and product are not constant.

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Answer 2

Let Cv and Cp denote the molar heat capacities of an ideal gas at constant volume and constant pressure respectively. Then Cp − Cv is a universal constant.

Explanation:

The universal constant:

Cp - Cv = R for ideal gas , Here, R is a gas constant of 8.314 J / K , Cv and Cp represent the molar heat capacities of an ideal gas at steady volume and pressure.

Option (a) ,(b) and (d) are incorrect which differs for monoatomic, diatomic or polyatomic gases.

The ratio of these two specific heats (Cp/Cv) is called the HEAT CAPACITY RATIO

On another hand, the ratio of both changes when the atomic nature of the gas changes.

Their quantity and product are also not stable.

Therefore, Cp - Cv is a constant.

Therefore the correct answer is Option (c) Cp − Cv