Questions similar to the following one are often found in Medical and Engineering entrance examination question papers:

**One mole of an ideal mono atomic gas is mixed with two moles of an ideal diatomic gas. The ratio of specific heats of the mixture is**

**(a) 1.5 (b) 1.4 (c) 10/6 (d) 15/11 (e) 19/13 **

You should remember that the values of molar specific heats at constant volume C_{v}) for mono atomic and diatomic gases are respectively (3/2)R and (5/2)R where R is universal gas constant. The values of molar specific heat at constant pressure C_{p}) are therefore (5/2)R and (7/2)R respectively, in accordance with Meyer’s relation [C_{p} – C_{v} =R].

Therefore, C_{v} of the mixture = [1×(3/2)R + 2×(5/2)R]/(1+2) = (13/6)R

C_{p }of the mixture = C_{v} + R = (19/6)R.

Ratio of specific heats of the mixture, γ = C_{p}/C_{v} = 19/13.

[Generally, if n_{1} moles of a gas having ratio of specific heats γ_{1} is mixed with n_{2} moles of a gas having ratio of specific heats γ_{2}, the ratio of specific heats of the mixture is given by the relation, (n_{1}+ n_{2})/(γ– 1)_{ }= n_{1}/( γ_{1} –1) + n_{2}/( γ_{2} –1). You can easily arrive at this result].

**If one mole of an ideal mono atomic gas is ****mixed with one mole of an ideal diatomic gas, the ratio of specific heats of the mixture is 1.5. **As an exercise, check this.

Now consider the following MCQ:

**The following sets of experimental values of C _{v} and C_{p }of a given sample of gas were reported by five groups of students. The unit used **

**is calorie**

**mole**

^{–}

^{1 }**K**

^{–}

^{1}**. Which set gives the most reliable values?**

**(a) C _{v} = 3, C_{p }= 4.5 (b) C_{v} = 2, C_{p }= 4 (c) C_{v} = 3, C_{p }= 4.9 (d) C_{v} = 2.5, C_{p }= 4.5 (e) C_{v} = 3, C_{p }= 4.2 **

Since the minimum value of C_{v} is (3/2)R which is the value for a mono atomic gas, when you express it in calorie mole^{–}^{1 }K^{–}^{1}, the minimum value is approximately 3. [R = 8.3 J mole^{–}^{1 }K^{–}^{1} = 2 calorie mole^{–}^{1 }K^{–}^{1}, approximately]. Options (b) and (d) are therefore not acceptable. Out of the remaining three options, (c) is the most reliable since C_{p} – C_{v} = R, which should be 2 calorie mole^{–}^{1 }K^{–}^{1} very nearly.

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