$A$ rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for the process is $TV^x =$ constant,then $x$ is

When air of the atmosphere rises up,it cools. Why?

An ideal gas at $27^{\circ} C$ is compressed adiabatically to $8/27$ of its original volume. If the ratio of specific heats is $\gamma = 5/3$,then the rise in temperature of the gas is: (in $K$)

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $27^{\circ}C$ to $37^{\circ}C$. If the ideal gas is composed of polyatomic molecules that have $4$ vibrational modes,which of the following is true?

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.

$A$ monoatomic gas $(\gamma = 5/3)$ is suddenly compressed to $1/8$ of its original volume adiabatically. The pressure of the gas will change to: