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11.Thermodynamics
medium

વાયુની આંતરિકઊર્જા $U$ અને કદ પ્રસરણાંક વચ્ચેનો સંબંધ

A

$U = \frac{{PV}}{{\gamma - 1}}$

B

$U = \frac{{P{V^\gamma }}}{{\gamma - 1}}$

C

$U = \frac{{PV}}{\gamma }$

D

$U = \frac{\gamma }{{PV}}$

Solution

$\Delta U = \mu \,{c_v}\Delta T$ ==> ${U_2} – {U_1} = \mu \,{c_v}({T_2} – {T_1})$

${T_1} = 0$ so ${U_1} = 0$ 

${T_2} = T$ and ${U_2} = U$

$U = \mu \,\,{c_v}T = \mu \,T \times {c_v}$$ = \frac{{PV}}{R} \times \frac{R}{{\gamma – 1}} = \frac{{PV}}{{\gamma – 1}}$

[$PV = \mu \,RT$                      $\therefore$ $\mu T = \frac{{PV}}{R}$ and ${c_v} = \frac{R}{{\gamma – 1}}$]

Standard 11
Physics

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