An ideal gas is expanded adiabatically at an initial temperature of 300 K. So, that its volume is doubled. The final temperature of the hydrogen gas is (γ=1.40)

Question

An ideal gas is expanded adiabatically at an initial temperature of 300 K. So, that its volume is doubled. The final temperature of the hydrogen gas is (&gamma;=1.40) (A) 227.36 K (B) 500.30 K (C) 454.76 K (D)  -47° C

Tardigrade Admin · Accepted Answer

For an adiabatic process T1 V1&gamma;-1=T2 V2&gamma;-1 ((T1/T2))=((V2/V1))&gamma;-1 ⇒ (T1/T2)=((V2/V1))&gamma;-1 (300/T2)=(2)&gamma;-1 (300/T2)=(2)1.4-1 T2=227.36 K

Q. An ideal gas is expanded adiabatically at an initial temperature of $300 K$ . So, that its volume is doubled. The final temperature of the hydrogen gas is $(γ = 1.40)$

$227.36 K$

$500.30 K$

$454.76 K$

$- 4 7^{\circ} C$

For an adiabatic process $T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$
$(\frac{T _{1}}{T _{2}}) = (\frac{V _{2}}{V _{1}})^{γ - 1}$
$\Rightarrow \frac{T _{1}}{T _{2}} = (\frac{V _{2}}{V _{1}})^{γ - 1}$
$\frac{300}{T _{2}} = (2)^{γ - 1}$
$\frac{300}{T _{2}} = (2)^{1.4 - 1}$
$T_{2} = 227.36 K$

Q. An ideal gas is expanded adiabatically at an initial temperature of 300K. So, that its volume is doubled. The final temperature of the hydrogen gas is (γ=1.40)

227.36K

500.30K

454.76K

−47∘C