Solveeit Logo
Login

Question

Question: An ideal gas at \(\gamma = \frac { 5 } { 3 }\), then the rise in temperature is...

An ideal gas at γ=53\gamma = \frac { 5 } { 3 }, then the rise in temperature is

A

450 K

B

375 K

C

225 K

D

405 K

Answer

375 K

Explanation

Solution

T2T1=(V1V2)γ−1⇒T2=300(278)53−1=300(278)23\frac { T _ { 2 } } { T _ { 1 } } = \left( \frac { V _ { 1 } } { V _ { 2 } } \right) ^ { \gamma - 1 } \Rightarrow T _ { 2 } = 300 \left( \frac { 27 } { 8 } \right) ^ { \frac { 5 } { 3 } - 1 } = 300 \left( \frac { 27 } { 8 } \right) ^ { \frac { 2 } { 3 } }

=300{(278)1/3}2=800(32)2=675K= 300 \left\{ \left( \frac { 27 } { 8 } \right) ^ { 1 / 3 } \right\} ^ { 2 } = 800 \left( \frac { 3 } { 2 } \right) ^ { 2 } = 675 K