Why is an increase in the temperature of a gas at constant volume and constant pressure not possible?

Which relation is correct for the given $P-V$ diagram?

Equal molar amounts of $H_2$ and $He$ are placed in two separate containers of equal volume at the same temperature. Their molar masses are $2$ and $4$ respectively. If the pressure of $H_2$ gas is $4 \ atm$,what will be the pressure of $He$ gas in atmospheres?

The adjoining figure shows graphs of pressure and volume of a gas at two temperatures $T_1$ and $T_2$. Which of the following is correct?

An engineer is given a fixed volume $V_m$ of metal with which to construct a spherical pressure vessel. Assuming the vessel has thin walls and is pressurized to its bursting point,the amount of gas the vessel can contain,$n$ (in moles),depends only on $V_m$ $(m^3)$,the temperature $T$ $(K)$,the ideal gas constant $R$ $(J/(K \cdot mol))$,and the tensile strength of the metal $\sigma$ $(N/m^2)$. Which of the following gives $n$ in terms of these parameters?

The temperature of a gas contained in a closed vessel of constant volume increases by $1^{\circ} C$ when the pressure of the gas is increased by $1 \%$. The initial temperature of the gas is