One gram-mole of an ideal gas A with the ratio of constant pressure and constant volume specific heats, \gamma_A = 5/3 is mixed with n gram-moles of another ideal gas B with \gamma_B = 7/5. If the \gamma for the mixture is 19/13 what will be the value of n ?

KVPY 2019 SB SX Exam Previous Papers

Question : 38 of 120

Marks: +1, -0

One gram-mole of an ideal gas A with the ratio of constant pressure and constant volume specific heats,

γ_A = 5/3

is mixed with n gram-moles of another ideal gas B with

γ_B = 7/5.

If the

γ

for the mixture is

19/13

what will be the value of n ?

Solution:

energy conservation

\f_1/2n_1RT+\f_2/2n_2RT_2=\f_\eq/2(n_1+ n_2 )RT

\f_\eq = {\f_1 n_1+ \f_2 n_2 }/{n_1+n_2}

⇒

2/{y_\eq-1}=(n_1/{n_1+n_2})(2/{y_1-1})

+(n_2/{n_1+n_2})(2/{y_2-1})

put

n_1 = 1

and

n_2 = n

⇒

n = 2

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