The following graph represents the $$T$$-$$V$$ curves of an ideal gas (where $$T$$ is the temperature and $$V$$ the volume) at three pressures $$P_1, P_2$$ and $$P_3$$ compared with those of Charles's law represented as dotted lines.

Then the correct relation is :

For the given cycle, the work done during isobaric process is:

A container of volume $$200 \mathrm{~cm}^3$$ contains 0.2 mole of hydrogen gas and 0.3 mole of argon gas. The pressure of the system at temperature $$200 \mathrm{~K}$$ ($$\mathrm{R}=8.3 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$$) will be :-

The temperature of a gas is $$-50^{\circ} \mathrm{C}$$. To what temperature the gas should be heated so that the rms speed is increased by $$3$$ times?