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Physics Question on Thermodynamics

A rigid diatomic ideal gas undergoes an adiabatic process at room temperature,. The relation between temperature and volume of this process is TVxTV^x = constant, then xx is :

A

53\frac{5}{3}

B

25\frac{2}{5}

C

23\frac{2}{3}

D

35\frac{3}{5}

Answer

25\frac{2}{5}

Explanation

Solution

For adiabatic process : TVγ−1TV^{\gamma -1} = constant
For diatomic process : γ−1=75−1\gamma -1 = \frac{7}{5} - 1
∴  x=25\therefore \; x = \frac{2}{5}