Question

If at `50^(@)C` and `75 cm` of mercury pressure, a definite mass of gas is compressed (i) slowly (ii) suddenly, than what will be the final pressure and temp. of the gas in each case, if the final volume is one fourth of the initial volume? `gamma= 1.5`.

Answer 1

Correct Answer - (i) `300 cm ; 50^(@)C` (ii) `600 cm ; 373^(@)C`
(a) When the gas is compressed slowly, the change is isothermal, `:. P_(2)V_(2)= P_(1)V_(1)`
or `P_(2)= (P_(1)V_(1))/(V_(2))= (75xxV_(1))/(V_(1)//4)= 300 cm of Hg`
Temp. remains constant at `50^(@)C`
(b) When the gas is compressed suddenly, the change is adiabatic
As `P_(2)V_(2)^(gamma)= P_(1)V_(1)^(gamma)`
`:. P_(2)=P_(1)((V_(1))/(V_(2)))^(gamma)`
`= 75(4)^(1.5)= 600` cm of Hg
Also, `T_(2)V_(2)^((gamma-1))= T_(1)V_(1)^((gamma-1))`
`T_(2)= T_(1)((V_(1))/(V_(2)))^((gamma-1))= 323(4)^((1.5-1))= 646K`
`= 646-273= 373^(@)C`