An ideal gas is suddenly compressed to (1/4) th of its initial volume. If the initial temperature of the gas is 27° C, then rise in temperature is (γ=1.5)

Question

An ideal gas is suddenly compressed to (1/4) th of its initial volume. If the initial temperature of the gas is 27° C, then rise in temperature is (&gamma;=1.5) (A) 300° C (B) 300 K (C) 327° C (D) Both (1) and (2)

Tardigrade Admin · Accepted Answer

T V-1= constant (T2/T1)=((V1/V2))&gamma;-1 (T2/300)=(4)1.5-1=2 T2=600 K Δ T=600-300 =300 K

Q. An ideal gas is suddenly compressed to $\frac{1}{4}$ th of its initial volume. If the initial temperature of the gas is $2 7^{\circ} C$ , then rise in temperature is $(γ = 1.5)$

$30 0^{\circ} C$

$300 K$

$32 7^{\circ} C$

Both $(1)$ and $(2)$

$T V^{- 1} =$ constant
$\frac{T _{2}}{T _{1}} = (\frac{V _{1}}{V _{2}})^{γ - 1}$
$\frac{T _{2}}{300} = (4)^{1.5 - 1} = 2$
$T_{2} = 600 K$
$Δ T = 600 - 300$
$= 300 K$

Q. An ideal gas is suddenly compressed to 41​ th of its initial volume. If the initial temperature of the gas is 27∘C, then rise in temperature is (γ=1.5)

300∘C

300K

327∘C

Both (1) and (2)