Question

An ideal gas at a pressure of 1 atmosphere and temperature of 27°C is compressed adiabatically until its pressure becomes 8 times the initial pressure. Then the final temperature is $\left( \text{Given}\gamma = \frac{3}{2} \right)$

• A. 627°C
• B. 527°C
• C. 427°C
• D. 327°C

Answer 1

Answer: (D)

327°C

Answer 2

Here, $P_{1} = 1atm,T_{1} = 27{^\circ}C = 27 + 273 = 300K$

$P_{2} = 8P_{1},T_{2} = ?,\gamma = \frac{3}{2}$

As change are adiabatic,

$\therefore{P_{1}}^{\gamma - 1}{T_{1}}^{- \gamma} = {P_{2}}^{\gamma - 1}{T_{2}}^{- \gamma}$

$\left( \frac{T_{2}}{T_{1}} \right)^{- \gamma} = \left( \frac{P_{1}}{P_{2}} \right)^{\gamma - 1}$

$T_{2} = 600K = (600 - 273){^\circ}C = 327{^\circ}C$