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11.Thermodynamics
normal
An ideal gas is expanding such that $PT^2$ = constant. The coefficient of volume expansion of the gas is :-
A
$1/T$
B
$2/T$
C
$3/T$
D
$4/T$
Solution
આદર્શ વાયુ માટે $PV = \mu RT$
$\therefore \,\,P\,\, = \,\,\frac{{\mu RT}}{V}$ તથા $\,P{T^2} = \,$ અચળ $\,\therefore \,\,\,\frac{{\mu RT}}{V}\,\,.\,\,{T^2}\,\, = $અચળ ${\text{ = k}}$
$\therefore \mu RT^{3} = kV … (1)$ $\therefore \mu R(3T^{2}dT) = kdV … (2) $
સમીકરણ $(2)$ ને $(1)$ વડે ભાગતા $\therefore \,\,\frac{{3\mu R{T^2}dT}}{{\mu R{T^3}}}\, = \,\,\frac{{kdV}}{{kV}}\,\,\,\,\,\therefore \,\,\frac{{3dT}}{T}\,\, = \,\,\frac{{dV}}{V}\,\,\,\,\,\therefore \,\,\frac{{dV}}{{VdT}}\,\, = \,\gamma \,\, = \,\,\frac{3}{T}$
Standard 11
Physics
