An ideal gas at 27° C is compressed adiabatically to (8/27) of its original volume. If γ=(5/3), then rise in temperature is

Question

An ideal gas at 27° C is compressed adiabatically to (8/27) of its original volume. If &gamma;=(5/3), then rise in temperature is (A) 375 K (B) 475 K (C) 575 K (D) 675 K

Tardigrade Admin · Accepted Answer

(300) V(5/3)-1=T2((8 V/27))(5/3)-1 ⇒ T2=300((9/4))=675 K Rise in temperature =675-300 =375 K

Q. An ideal gas at $2 7^{\circ} C$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. If $γ = \frac{5}{3}$ , then rise in temperature is

375 K

475 K

575 K

675 K

$(300) V^{\frac{5}{3} - 1} = T_{2} (\frac{8 V}{27})^{\frac{5}{3} - 1}$
$\Rightarrow T_{2} = 300 (\frac{9}{4}) = 675 K$
Rise in temperature $= 675 - 300$
$= 375 K$

Q. An ideal gas at 27∘C is compressed adiabatically to 278​ of its original volume. If γ=35​, then rise in temperature is