Which one of the following represents correctly the variation of volume (V) of an ideal gas with temperature $$(\mathrm{T})$$ under constant pressure conditions?

$$\mathrm{dQ}$$ is the heat energy supplied to an ideal gas under isochoric conditions. If $$\mathrm{dU}$$ and $$\mathrm{dW}$$ denote the change in internal energy and the work done respectively then

A black body at temperature $$127^{\circ} \mathrm{C}$$ radiates heat at the rate of $$5 \mathrm{~cal} / \mathrm{cm}^2 \mathrm{~s}$$. At a temperature $$927^{\circ} \mathrm{C}$$, its rate of emission in units of $$\mathrm{cal} / \mathrm{cm}^2 \mathrm{~s}$$ will be

A Carnot engine has the same efficiency between (i) $$100 \mathrm{~K}$$ and $$600 \mathrm{~K}$$ and (ii) $$\mathrm{T} \mathrm{K}$$ and $$960 \mathrm{~K}$$. The temperature $$\mathrm{T}$$ in kelvin of the sink is