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

The pressure and density of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$ changes adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d}=32$, then $\frac{P^{\prime}}{P}$ is:

$Assertion :$ Air quickly leaking out of a balloon becomes cooler.
$Reason :$ The leaking air undergoes adiabatic expansion.

In an adiabatic process $90 \ J$ of work is done on the gas. The change in internal energy of the gas is ....... $J$.

By what factor should the volume of an ideal gas $(\gamma = 1.5)$ be increased through an adiabatic expansion so that its $rms$ speed becomes half?

$A$ reversible adiabatic path on a $P-V$ diagram for an ideal gas passes through state $A$ where $P = 0.7 \times 10^5 \, N/m^2$ and $V = 0.0049 \, m^3$. The ratio of specific heats of the gas is $1.4$. The slope of the path at $A$ is: