ThermodynamicsMedium
Question
The volume of an ideal gas increases 8 times and temperature becomes $(1/4)^{\text{th~}}$ of initial temperature during a reversible change. If there is no exchange of heat in this process ( $\Delta Q = 0$ ) then identify the gas from the following options (Assuming the gases given in the options are ideal gases) :
Options
A.${CO}_{2}$
B.$O_{2}$
C.${NH}_{3}$
D.He
Solution
${PV}^{\gamma} =$ constant
${TV}^{\gamma - 1} =$ constant
$${{TV}^{\gamma - 1} = \left( \frac{T}{4} \right)(8\text{ }V)^{(\gamma - 1)} }{4 = 8^{(\gamma - 1)} }{2^{2} = 2^{3\gamma - 3} }{2 = 3(\gamma - 1) }{\gamma = \frac{5}{3} }$$Gas is a monoatomic gas
Answer is He .
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