In a thermodynamic system,$W$ represents the work done by the system and $\Delta U$ is the increase in internal energy. Which of the following statements is $TRUE$?

During the adiabatic expansion of $2 \, moles$ of a gas,the internal energy was found to have decreased by $100 \, J$. The work done by the gas in this process is ..... $J$.

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.)

During an adiabatic process,if the pressure of a gas is found to be proportional to the cube of its absolute temperature,then the ratio of $\frac{C_p}{C_V}$ for the gas is:

$A$ cycle tyre bursts suddenly. What is the type of this process?

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