The pressure $$(\mathrm{P})$$ and temperature ($$\mathrm{T})$$ relationship of an ideal gas obeys the equation $$\mathrm{PT}^{2}=$$ constant. The volume expansion coefficient of the gas will be :

Heat is given to an ideal gas in an isothermal process.

A. Internal energy of the gas will decrease.

B. Internal energy of the gas will increase.

C. Internal energy of the gas will not change.

D. The gas will do positive work.

E. The gas will do negative work.

Choose the correct answer from the options given below :

Heat energy of 184 kJ is given to ice of mass 600 g at $$-12^\circ \mathrm{C}$$. Specific heat of ice is $$\mathrm{2222.3~J~kg^{-1^\circ}~C^{-1}}$$ and latent heat of ice in 336 $$\mathrm{kJ/kg^{-1}}$$

A. Final temperature of system will be 0$$^\circ$$C.

B. Final temperature of the system will be greater than 0$$^\circ$$C.

C. The final system will have a mixture of ice and water in the ratio of 5 : 1.

D. The final system will have a mixture of ice and water in the ratio of 1 : 5.

E. The final system will have water only.

Choose the correct answer from the options given below :

At 300 K, the rms speed of oxygen molecules is $$\sqrt {{{\alpha + 5} \over \alpha }} $$ times to that of its average speed in the gas. Then, the value of $$\alpha$$ will be

(used $$\pi = {{22} \over 7}$$)