A gas is suddenly compressed to `1/4th` of its original volume. Caculate the rise in temperature when original temperature is `27^(@)C. gamma= 1.5`.

Options

A. `300^(@)C`
B. `350^(@)C`
C. `400^(@)C`
D. `450^(@)C`

Answer

A

Explanation

Let the initial volume `V_(1)=V`
Final valume `V_(2)=v//4`
Here , initial temperature
`T_(1)=27^(@)C=273+27=300K `
Let `T_(2)` K be the final temperature after compression. Since the change is adiabatic
`T_(1)V_(1)^(y-2)=T_(2)V_(2)^(y-2)`
`T_(2)=T_(1)((V_(1))/(V_(2)))^(y-1)=300((V)/(v//4))^(1.5-2)`
`=300(4)^(1//2)=300xx2=600K`
`T_(2)=600-273=327^(@)C`
`therefore "Rise in temperature"=317-27=300^(@)C`