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 =(μ 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:

Question

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 =(μ R ( T 2- T 1)/1-&gamma;), where &gamma;=( 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: (A) Both statement—I and statement-II are true. (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.

Tardigrade Admin · Accepted Answer

W text adiabatic =( NR ( T f - T i )/1-&gamma;) arrow statment 1 Q = W +Δ U 0= W +Δ U Δ U =- W If work is done on the gas, i.e. work is negative ∴ Δ U is positive. ∴ Temperature will increase.

Both statement—I and statement-II are true.

Both statement—I and statement-II are false.

Statement-I is true but statement-II is false.

Statement-I is false but statement-II is true.

Wadiabatic ​=1−γNR(Tf​−Ti​)​→ statment 1 Q=W+ΔU 0=W+ΔU ΔU=−W If work is done on the gas, i.e. work is negative ∴ΔU is positive. ∴ Temperature will increase.

$W_{adiabatic} = \frac{NR ( T _{f} - T _{i} )}{1 - γ} \to$ statment $1$
$Q = W + Δ U$
$0 = W + Δ U$
$Δ U = - W$
If work is done on the gas, i.e. work is negative
$∴ Δ U$ is positive.
$∴$ Temperature will increase.