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Question: Mayer’s formula \({C_p} - {C_v} = \dfrac{R}{J}\) is for \(1\) gm mole of a gas. If we consider n gm ...

Mayer’s formula Cp−Cv=RJ{C_p} - {C_v} = \dfrac{R}{J} is for 11 gm mole of a gas. If we consider n gm mol. of the gas the formula is (in heat units):
A. Cp−Cv=nRJ{C_p} - {C_v} = \dfrac{{nR}}{J}
B. Cp−Cv=RJ{C_p} - {C_v} = \dfrac{R}{J}
C. n(Cp−Cv)=RJn\left( {{C_p} - {C_v}} \right) = \dfrac{R}{J}
D. Cp−Cv=RnJ{C_p} - {C_v} = \dfrac{R}{{nJ}}

Explanation

Solution

Here we are given the Mayer’s formula for one gm mole of a gas and are asked to find n gm mol of the gas formula. Here we will place the values for “n” gm mole of a gas and simplify for the resultant answer in the standard formula.

Complete step by step answer:
Mayer’s formula is derived by using the difference between the specific heat of a gas at the constant pressure (Cp)({C_p}) and its specific heat at constant volume (Cv)({C_v}) which is equal to the universal gas constant (R) divided with the molecular weight (M) of the gas expressed in “J”.
Mayer’s formula is expressed by –
Cp−Cv=RJ{C_p} - {C_v} = \dfrac{R}{J} (For one gm mole of a gas)
Similarly for “n” gm mole of the gas gives –
Cp−Cv=nRJ{C_p} - {C_v} = \dfrac{{nR}}{J}

So, the correct answer is “Option A”.

Note:
Always remember the basic standard formulas stating the correlation between the constant pressure, volume and temperature. Generally they are known as the PVT equations. To solve these types of word problems always remember the basic five types of gas laws which deal with how gases behave with respect to the pressure, volume and temperature.
- Boyle’s law
- Charles’ law
- Gay-Lussac’s law
- Combined law
- Ideal Gas law
Always remember all the terminologies and the major and minor differences among each of the laws along with the conditions and the standard formula under each type of laws.