An ideal gas at 27° C is compressed adiabatically to 8/27 of its original volume. The rise in temperature is (Take γ =5/3)

Question

An ideal gas at 27° C is compressed adiabatically to 8/27 of its original volume. The rise in temperature is (Take &gamma; =5/3) (A) 275 K (B) 375 K (C) 475 K (D) 175 K

Tardigrade Admin · Accepted Answer

TV&gamma;-1= constant (adiabatic). =(300)(V0)2/3=(Vf)2/3 T T=300 ( (27/8) )2/3 =300 × ( (3/2) )3 × (2/3)= (300 × 9/4)= 675 K Temperature rise = 675-300=375 K

Q. An ideal gas at $2 7^{\circ} C$ is compressed adiabatically to 8/27 of its original volume. The rise in temperature is (Take $γ = 5/3$ )

275 K

375 K

475 K

175 K

$T V^{γ - 1} =$ constant (adiabatic).
$= (300) (V_{0})^{2/3} = (V_{f})^{2/3} T$
$T = 300 (\frac{27}{8})^{2/3} = 300 \times (\frac{3}{2})^{3 \times \frac{2}{3}} = \frac{300 \times 9}{4} = 675 K$
Temperature rise = 675-300=375 K

Q. An ideal gas at 27∘C is compressed adiabatically to 8/27 of its original volume. The rise in temperature is (Take γ=5/3)