Question 583: Thermodynamics & KTG

Question

The pressure $$\mathrm{P}_{1}$$ and density $$\mathrm{d}_{1}$$ of diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ changes suddenly to $$\mathrm{P}_{2}\left(>\mathrm{P}_{1}\right)$$ and $$\mathrm{d}_{2}$$ respectively during an adiabatic process. The temperature of the gas increases and becomes ________ times of its initial temperature. (given $$\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}=32$$)

Accepted Answer

$${P_1}V_1^\gamma  = {P_2}V_2^2$$
$${{{P_1}} \over {d_1^\gamma }} = {{{P_2}} \over {d_2^\gamma }}$$
$${{{d_1}{T_1}} \over {d_1^\gamma }} = {{{d_2}{T_2}} \over {d_2^\gamma }}$$
$${T_2} = {\left( {{{{d_2}} \over {{d_1}}}} \right)^{\gamma  - 1}}{T_1}$$
$$ = {(32)^{{2 \over 5}}}{T_1}$$
$${T_2} = 4\,{T_1}$$

Thermodynamics & KTG

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