$A$ piston is slowly pushed into a metal cylinder containing an ideal gas. Which of the following statements is/are incorrect?

One mole of the ideal gas goes through the process $p=p_0\left[1-\alpha\left(\frac{V}{V_0}\right)^3\right]$, where $p$ and $V$ are pressure and volume, $p_0, V_0$ and $\alpha$ are constants. If the maximum attainable temperature of the gas is $\left(\frac{3}{4}\right) \frac{p_0 V_0}{R}$, then the value of $\alpha$ is

Following statements are given:
$(1)$ The average kinetic energy of a gas molecule decreases when the temperature is reduced.
$(2)$ The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
$(3)$ The average kinetic energy of a gas molecule decreases with increase in volume.
$(4)$ Pressure of a gas increases with increase in temperature at constant volume.
$(5)$ The volume of gas decreases with increase in temperature.
Choose the correct answer from the options given below:

$N$ moles of a diatomic gas in a cylinder are at a temperature $T$. Heat is supplied to the cylinder such that the temperature remains constant but $n$ moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas?

Which of the following statements is true?

$A$ monoatomic gas of mass $4.0 \, g$ is kept in an insulated container. The container is moving with a velocity of $30 \, m/s$. If the container is suddenly stopped,then the change in temperature of the gas (where $R$ is the gas constant) is given by $\frac{x}{3R}$. The value of $x$ is ..........