An ideal gas at 27°C is compressed adiabatically to 8/27 of its original volume. If γ = 5/3, then the rise in temperature is

Q: An ideal gas at 27°C is compressed adiabatically to 8/27 of its original volume. If γ = 5/3, then the rise in temperature is

(a) 450°C

(b) 375°C

(d) 405°C

Ans: (b)

Sol: T₁ = 27 + 273 = 300 K, V₁ = V, V₂ = (8/27) V, T₂ = ?

$\large T_1 V_1^{\gamma -1} = T_2 V_2^{\gamma -1} $

$\large T_2 = T_1 (\frac{V_1}{V_2})^{\gamma -1} $

$\large T_2 = 300 \times \frac{V}{8V/27}^{5/3 -1} $

$\large T_2 = 300 \times (\frac{27}{8})^{2/3}$

$\large T_2 = 300 \times (\frac{3}{2})^2 $

T₂ = 675 K

∆T = T₂ – T₂

∆T = 675 – 300 = 375 K

or , ∆T = 375°C