JEE MAIN - Physics (2018 - 16th April Morning Slot - No. 12)
Two moles of helium are mixed with n moles of hydrogen. If $${{Cp} \over {Cv}} = {3 \over 2}$$ for the mixture, then the value of n is :
1
3
2
3 / 2
Explanation
$${{{C_p}} \over {{C_v}}} = {{{f_{mix}} + 2} \over {{f_{mix}}}} = {3 \over 2}$$
$$ \Rightarrow $$$$\,\,\,$$ fmix = 4
As, fmix = $${{{n_1}{f_1} + {n_2}{f_2}} \over {{n_1} + {n_2}}}$$
$$ \Rightarrow $$$$\,\,\,$$ 4 = $${{2 \times 3 + n \times 5} \over {2 + n}}$$
$$ \Rightarrow $$$$\,\,\,$$ n = 2 moles.
$$ \Rightarrow $$$$\,\,\,$$ fmix = 4
As, fmix = $${{{n_1}{f_1} + {n_2}{f_2}} \over {{n_1} + {n_2}}}$$
$$ \Rightarrow $$$$\,\,\,$$ 4 = $${{2 \times 3 + n \times 5} \over {2 + n}}$$
$$ \Rightarrow $$$$\,\,\,$$ n = 2 moles.
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