NEET UG 2010 — Thermodynamics

The thermo emf $E$ in volt of a certain thermo-couple is found to vary with temperature difference $\theta$ in ${ }^{\circ} \mathrm{C}$ between the two junctions according to the relation $E=30 \theta-\frac{\theta^2}{15}$ The neutral temperature for the thermo-couple will be

If $\mathrm{C}_{\mathrm{p}}$ and $\mathrm{C}_{\mathrm{V}}$ denote the specific heats (per unit mass) of an ideal gas of molecular weight $M$ where $R$ is the molar gas constant.

If $\Delta \mathrm{U}$ and $\Delta \mathrm{W}$ represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?

A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat $Q$ in time t. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod when placed in thermal contact with the two reservoirs in time $\mathrm{t}$ ?

A monoatomic gas at pressure $p_1$ and $V_1$ is compressed adiabatically to $\frac{1}{8}$ th its original volume. What is the final pressure of the gas?

The total radiant energy per unit area, normal to the direction of incidence, received at a distance $\mathrm{R}$ from the centre of a star of radius $r$, whose outer surface radiates as a black body at a temperature $T \mathrm{~K}$ is given by (where $\sigma$ is Stefan's constant)