Question

One mole of monoatomic gas and one mole of diatomic gas is present in a mixture. Find out ratio of heat capacities at constant volume and constant

pressure \(\left(i.e.\frac{C_v}{C_P}\right)\)

(1)  \(\frac{2}{3}\)

(2)  \(\frac{7}{5}\)

(3)  \(\frac{5}{7}\)

(4)  \(\frac{3}{5}\)

Answer 1

Correct answer is:  (1) \(\frac{2}{3}\)

\(C_V=\frac{1\left(\frac{3R}{2}\right)+1\left(\frac{5R}{2}\right)}{2}\)

\(=\frac{8R}{4}=2R\)

\(C_P=\frac{1\left(\frac{5R}{2}\right)+1\left(\frac{7R}{2}\right)}{2}\)

\(=\frac{12R}{4}=3R\)

\(\frac{C_V}{C_P}=\frac{2R}{3R}\)

\(=\frac{2}{3}\)