An ideal gas in a cylinder is compressed adiabatically to one-third of its original volume. $A$ work of $45 \,J$ is done on the gas by the process. The change in internal energy of the gas and the heat flowed into the gas, respectively are

During an adiabatic process,the pressure of the gas is found to be proportional to the cube of its absolute temperature. The ratio $C_P/C_V = \gamma$ for the gas is:

$A$ monoatomic gas is filled in a cylindrical container with a piston at temperature $T_1$. It undergoes an adiabatic expansion such that its temperature becomes $T_2$. If $L_1$ and $L_2$ are the lengths of the gas column before and after the expansion respectively,then $T_1/T_2$ is equal to:

In case of an adiabatic process,the correct relation in terms of pressure $p$ and density $\rho$ of a gas is:

An ideal gas,undergoing adiabatic change,has which of the following pressure-temperature relationships?

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1:$ In an adiabatic process,the change in internal energy of a gas is equal to the work done on/by the gas in the process.
Statement $2:$ The temperature of a gas remains constant in an adiabatic process.