1. Tardigrade
  2. Question
  3. Physics
  4. 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 Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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 $W =\frac{\mu R \left( T _{2}- T _{1}\right)}{1-\gamma}$, where $\gamma=\frac{ C _{ P }}{ C _{ V }} \quad$ 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:

JEE MainJEE Main 2022Thermodynamics

Solution:

$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.