Helium at 27° C has a volume 8 litres. It is suddenly compressed to a volume of 1 litre. The temperature of the gas will be (V=5 / 3)

Question

Helium at 27° C has a volume 8 litres. It is suddenly compressed to a volume of 1 litre. The temperature of the gas will be (V=5 / 3) (A) 9327° C (B)  1200° C  (C)  927° C  (D)  108° C

Tardigrade Admin · Accepted Answer

T1 V1&gamma;-1 =T2 V2&gamma;-1 T2 =((V1/V2))&gamma;-1 T1 T2 =((V1/V2))(5/3)-1 × 300 T2 =((8/1))2 / 3 × 300 =4 × 300 =1200 K =927° C

Q. Helium at $2 7^{\circ} C$ has a volume $8$ litres. It is suddenly compressed to a volume of $1$ litre. The temperature of the gas will be $(V = 5/3)$

$932 7^{\circ} C$

$120 0^{\circ} C$

$92 7^{\circ} C$

$10 8^{\circ} C$

$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$
$T_{2} = (\frac{V _{1}}{V _{2}})^{γ - 1} T_{1}$
$T_{2} = (\frac{V _{1}}{V _{2}})^{\frac{5}{3} - 1} \times 300$
$T_{2} = (\frac{8}{1})^{2/3} \times 300$
$= 4 \times 300$
$= 1200 K = 92 7^{\circ} C$

Q. Helium at 27∘C has a volume 8 litres. It is suddenly compressed to a volume of 1 litre. The temperature of the gas will be (V=5/3)

9327∘C

1200∘C

927∘C

108∘C