A given ideal gas with γ = (Cp/Cv) = 1.5 at a temperature T. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be

Question

A given ideal gas with &gamma; = (Cp/Cv) = 1.5 at a temperature T. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be (A) 2√2T (B) 4 T (C) 2 T (D) 8 T

Tardigrade Admin · Accepted Answer

TV&gamma;-1 = constant T1V1&gamma;-1 = T2V2&gamma;-1 ⇒ T (V)1/2 = T2 ((V/4))1/2 [∵ &gamma; = 1.5, T1 =T, V1 = V and V2 = (V/4)] ∴ T2 = ((4V/V))1/2 T = 2T

Q. A given ideal gas with $γ = \frac{C _{p}}{C _{v}} = 1.5$ at a temperature $T$ . If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be

$22 T$

$4 T$

$2 T$

$8 T$

$T V^{γ - 1} =$ constant
$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$
$\Rightarrow T (V)^{1/2} = T_{2} (\frac{V}{4})^{1/2}$
$[∵ γ = 1.5, T_{1} = T, V_{1} = V an d V_{2} = \frac{V}{4}]$
$∴ T_{2} = (\frac{4 V}{V})^{1/2} T = 2 T$

Q. A given ideal gas with γ=Cv​Cp​​=1.5 at a temperature T. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be

22​T

4T

2T

8T