Question 497: Thermodynamics & KTG

Question

1 mole of a gas with $$\gamma  = 7/5$$ is mixed with $$1$$ mole of a gas with $$\gamma  = 5/3,$$ then the value of $$\gamma $$ for the resulting mixture is

Accepted Answer

If $${n_1}$$ moles of adiabatic exponent $${\gamma _1}$$ is mixed with $${n_2}$$ moles of adiabatic exponent $${\gamma _2}$$ then the adiabatic component of the resulting mixture is given by
$${{{n_1} + {n_2}} \over {\gamma  - 1}} = {{{n_1}} \over {{\gamma _1} - 1}} + {{{n_2}} \over {{\gamma _2} - 1}}$$
$${{1 + 1} \over {\gamma  - 1}} = {1 \over {{7 \over 5} - 1}} + {1 \over {{5 \over 3} - 1}}$$
$$	herefore$$ $${2 \over {\gamma  - 1}} = {5 \over 2} + {3 \over 2} = 4$$
$$	herefore$$ $$2 = 4\gamma  - 4 \Rightarrow \gamma  = {6 \over 4} = {3 \over 2}$$

Answer

$$7/5$$

Answer

$$2/5$$

Answer

$$3/2$$

Answer

$$12/7$$

Thermodynamics & KTG

1 mole of a gas with $\gamma = 7/5 is mixed with 1 mole of a gas with \gamma = 5/3, then the value of \gamma $ for the resulting mixture is

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