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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
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.
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.
