AP EAMCET20227 Jul 2022Evening ShiftPhysicsThermodynamicsActual
A monoatomic gas ( = 5 3 ) at a pressure of 4 ~atm is compressed adiabatically so that its temperature rises from 27^ C to 327^ C . The pressure of the gas in its final state is
Options
- A2^ 5 3 ~atm
- B2^ 10 3 ~atm
- C2^ 5 2 atm
- D2^ 9 2 ~atm
Correct answer
D. 2^ 9 2 ~atm
Step-by-step solution
(1) For an adiabatic change, aligned & p V^ = constant & T^ p^ 1- = constant or T₁^ , p₁^ 1- =T₂^ p₂^ 1- & p₂^ 1- = ( T₁ T₂ )^ p₁^ 1- & p₂= ( T₁ T₂ )^ 1- p₁ aligned Here, aligned & p₁=4 ~atm ; =5 / 3 & T₁=27^ C =300 ~K & T₂=327^ C =600 ~K aligned Now, substituting values in Eq. (i), we get aligned p₂ & = ( 300 600 )^ 5 / 3 1-5 / 3 4= ( 1 2 )^ -5 2 2^2 & =2^ 2+ 5 2 =2^ 9 2 aligned Hence, the pressure of the gas in its final state is 2^ 9 / 2 ~atm .