Which one is the correct option for the two different thermodynamic processes ?

A tyre filled with air $({27^o}C,$ and $2$ atm) bursts, then what is temperature of air ……. $^oC$ $(\gamma = 1.5)$

The slopes of isothermal and adiabatic curves are related as

Check the statement are trrue or false :

$1.$ For an adiabatic process $T{V^{\gamma  – 1}}$ $=$ constant.

$2.$ Charging process of battery is a reversible process.

$3.$ Water falls below from height is a reversible process.

$4.$ Internal energy, volume and mass are intensive variable while pressure, temperature and density are extensive variables.

A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, $C_v=2 R$. Here, $R$ is the gas constant. Initially, each side has a volume $V_0$ and temperature $T_0$. The left side has an electric heater, which is turned on at very low power to transfer heat $Q$ to the gas on the left side. As a result the partition moves slowly towards the right reducing the right side volume to $V_0 / 2$. Consequently, the gas temperatures on the left and the right sides become $T_L$ and $T_R$, respectively. Ignore the changes in the temperatures of the cylinder, heater and the partition.

($1$) The value of $\frac{T_R}{T_0}$ is

$(A)$ $\sqrt{2}$ $(B)$ $\sqrt{3}$ $(C)$ $2$ $(D)$ $3$

($2$) The value of $\frac{Q}{R T_0}$ is

$(A)$ $4(2 \sqrt{2}+1)$ $(B)$ $4(2 \sqrt{2}-1)$ $(C)$ $(5 \sqrt{2}+1)$ $(D)$ $(5 \sqrt{2}-1)$

Give the answer or qution ($1$) and ($2$)