When air of the atmosphere rises up it cools. Why ?

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature $T _1$, pressure $P_1$ and volume $V_1$ and the spring is in its relaxed state. The gas is then heated very slowly to temperature $T_2$, pressure $P _2$ and volume $V _2$. During this process the piston moves out by a distance $x$. Ignoring the friction between the piston and the cylinder, the correct statement$(s)$ is(are)

$(A)$ If $V_2=2 V_1$ and $T_2=3 T_1$, then the energy stored in the spring is $\frac{1}{4} P_1 V_1$

$(B)$ If $V_2=2 V_1$ and $T_2=3 T_1$, then the change in internal energy is $3 P_1 V_1$

$(C)$ If $V_2=3 V_1$ and $T_2=4 T_1$, then the work done by the gas is $\frac{7}{3} P_1 V_1$

$(D)$ If $V_2=3 V_1$ and $T_2=4 T_1$, then the heat supplied to the gas is $\frac{17}{6} P_1 V_1$

In thermodynamic processes which of the following statements is not true?

The equation of state for a gas is given by $PV = nRT + \alpha V$, where $n$ is the number of moles and $\alpha $ is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are $T_o$ and $P_o$ respectively. The work done by the gas when its temperature doubles isobarically will be

Write equation for work done for compression for an ideal gas.

A cycle tyre bursts suddenly. This represents an