Temperature of a body $\theta$ is slightly more than the temperature of the surrounding $\theta_0$. Its rate of cooling $(R)$ versus temperature of the body $(\theta)$ is plotted. Its shape would be

The speed distribution for a sample of $$\mathrm{N}$$ gas particles is shown below. $$\mathrm{P}(\mathrm{v})=0$$ for $$\mathrm{v}>2 \mathrm{v}_0$$. How many particles have speeds between $$1.2 \mathrm{v}_0$$ and $$1.8 \mathrm{v}_0$$ ?

The internal energy of a thermodynamic system is given by $$U=a s^{4 / 3} V^\alpha$$ where $$\mathrm{s}$$ is entropy, $$\mathrm{V}$$ is volume and '$$\mathrm{a}$$' and '$$\alpha$$' are constants. The value of $$\alpha$$ is

Six molecules of an ideal gas have velocities 1, 3, 5, 5, 6 and 5 m/s respectively. At any given temperature, if $$\mathrm{\overline V}$$ and $$\mathrm{V_{rms}}$$ represent average and rms speed of the molecules, then