A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $$\theta $$ along the length $$x$$ of the bar from its hot end is best described by which of the following figures?

Statement - 1: The temperature dependence of resistance is usually given as $$R = {R_0}\left( {1 + \alpha \,\Delta t} \right).$$ The resistance of wire changes from $$100\Omega $$ to $$150\Omega $$ when its temperature is increased from $${27^ \circ }C$$ to $${227^ \circ }C$$. This implies that $$\alpha = 2.5 \times {10^{ - 3}}/C.$$

Statement - 2: $$R = {R_0}\left( {1 + \alpha \,\Delta t} \right)$$ is valid only when the change in the temperature $$\Delta T$$ is small and $$\Delta T = \left( {R - {R_0}} \right) < < {R_0}.$$

Two moles of helium gas are taken over the cycle $$ABCD,$$ as shown in the $$P$$-$$T$$ diagram.

The work done on the gas in taking it from $$D$$ to $$A$$ is :

One $$kg$$ of a diatomic gas is at a pressure of $$8 \times {10^4}\,N/{m^2}.$$ The density of the gas is $$4kg/{m^3}$$. What is the energy of the gas due to its thermal motion ?