Question

`1mm^3` of a gas is compressed at 1 atmospheric pressure and temperature `27^@C` to `627^@C`. What is the final pressure under adiabatic condition `(gamma` for the gas `=1.5`)
A. `27xx10^5(N)/(m^2)`
B. `80xx10^5(N)/(m^2)`
C. `36xx10^5(N)/(m^2)`
D. `56xx10^5(N)/(m^2)`

Answer 1

Correct Answer - A
`P_1=1atm,T_1=27^@C=27+273=300K`
`T_2=627^@C=627+273=900K,P_2=?`
`(T_1^(gamma))/(P_1^(gamma-1))=(T_1^(gamma))/(P_2^(gamma-1))`
`((P_2)/(P_1))^(gamma-1)=((T_2)/(T_1))^(gamma)`
`(P_2)/(P_1)=((T_2)/(T_1))^((gamma)/(gamma-1))=((900)/(300))^(((3)/(2))/((3)/(2)-1))=(3)^2=27`
`P_2=27P_1=27xx1=27atm=27xx10^5(N)/(m^2)`