$A$ gas is compressed adiabatically. Which one of the following statements is $NOT$ true?

$\Delta U + \Delta W = 0$ is valid for

The equation of state of $n$ moles of a non-ideal gas can be approximated by the equation $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$,where $a$ and $b$ are constant characteristics of the gas. Which of the following can represent the equation of a quasistatic adiabat for this gas? (Assume that $C_V$,the molar heat capacity at constant volume,is independent of temperature.)

$A$ 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:

One mole of an ideal gas at an initial temperature of $T$ $K$ does $6R$ of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $5/3$,the final temperature of the gas will be $(R=8.31 \ J \ mole^{-1} \ K^{-1})$.

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