$A$ monoatomic ideal gas is compressed adiabatically to $\left(\frac{1}{27}\right)$ of its initial volume. If the initial temperature of the gas is $T \ K$ and the final temperature is $xT \ K$, the value of $x$ is:

The $P-V$ graph of an ideal gas cycle is shown. The adiabatic process is described by the region

$A$ monoatomic ideal gas, initially at temperature $T_1$, is enclosed in a cylinder fitted with a massless, frictionless piston. By releasing the piston suddenly, the gas is allowed to expand adiabatically to a temperature $T_2$. If $L_1$ and $L_2$ are the lengths of the gas columns before and after expansion respectively, then $(T_2 / T_1)$ is given by

Is it possible to increase the temperature of a gas without adding heat to it? Explain.

The $P-V$ diagram for two gases during an adiabatic process is shown in the figure. Curves $A$ and $B$ correspond to:

In an adiabatic expansion,which of the following is true?