If an ideal gas at 27 °C is compressed suddenly to one fourth of its initial volume, then rise in its temperature is (γ = 7/5)

Question

If an ideal gas at 27 °C is compressed suddenly to one fourth of its initial volume, then rise in its temperature is (&gamma; = 7/5)  (A)  222.33 K  (B)  233.33 K  (C)  244.33 K  (D)  255.33 K

Tardigrade Admin · Accepted Answer

Here, T1 = 27°C= 27 +273 = 300 K V2 = (V1/4) As the gas is compressed suddenly, then the process is adiabatic, then TV&gamma;-1 = constant ⇒ T1 V1 &gamma;-1 = T2 V2 &gamma;-1 or T2 =T1 ((V1/V2)) &gamma;-1 = 300 ((V1 /V1/4))(7/5) -1 = 300 × (4)2/5 = 522.33 K Hence, Change in temperature ⇒ Δ T =T2 -T1 = 522.33 -300 = 222.33 K

Q. If an ideal gas at $2 7^{\circ} C$ is compressed suddenly to one fourth of its initial volume, then rise in its temperature is $(γ = 7/5)$

$222.33 K$

$233.33 K$

$244.33 K$

$255.33 K$

Q. If an ideal gas at 27∘C is compressed suddenly to one fourth of its initial volume, then rise in its temperature is (γ=7/5)

222.33K

233.33K

244.33K

255.33K

Q. If an ideal gas at $2 7^{\circ} C$ is compressed suddenly to one fourth of its initial volume, then rise in its temperature is $(γ = 7/5)$

$222.33 K$

$233.33 K$

$244.33 K$

$255.33 K$