Given below are two statement Statement -I: What μ amount of an ideal gas undergoes adiabatic change from state ( P 1, V 1, T 1) to state ( P 2, V 2, T 2), the work done is W = 1 R ( T 2- T 1) 1-γ, where γ= C P C V and R = universal gas constant, Statement -II: In the above case. when work is done on the gas. the temperature of the gas would rise. Choose the correct answer from the options given below

(B) Both statement -I and statement -II are false.

(C) Statement -I is true but statement -II is false.

(D) Statement -I is false but statement -II is true.

JEE Mains · Physics · STD 11 - Thermodynamics

Given below are two statement Statement \(-I\) : What \(\mu\) amount of an ideal gas undergoes adiabatic change from state \(\left( P _{1}, V _{1}, T _{1}\right)\) to state \(\left( P _{2}, V _{2}, T _{2}\right)\), the work done is \(W =\frac{1 R \left( T _{2}- T _{1}\right)}{1-\gamma}\), where \(\gamma=\frac{ C _{ P }}{ C _{ V }}\) and \(R =\) universal gas constant, Statement \(-II\) : In the above case. when work is done on the gas. the temperature of the gas would rise. Choose the correct answer from the options given below

Pick an option to check your answer.

Verified Solution

Correct Answer

(A) Both statement \(-I\) and statement \(-II\) are true.

Detailed explanation

\(W _{\text {adiabatic }}=\frac{ NR \left( T _{f}- T _{ i }\right)}{1-\gamma} \rightarrow\) statment \(1\)

\(Q=W+\Delta U\)

\(0= W +\Delta U\)

\(\Delta U =- W\)

If work is done on the gas, i.e. work is negative

\(\therefore \Delta U\) is positive.

\(\therefore\) Temperature will increase.

Same subject

From JEE Mains