Thermal Properties of Matter

Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperatures $T_1$ and $T_2$, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B?

A piece of ice (heat capacity = 2100 J kg⁻¹ °C⁻¹ and latent heat = $3.36\times10^5$ J kg⁻¹) of mass m grams is at −5°C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is

A metal rod AB of length $10x$ has its one end A in ice at 0°C and the other end B in water at 100°C. If a point P on the rod is maintained at 400°C, then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of evaporation of water is 540 cal/g and latent heat of melting of ice is 80 cal/g. If the point P is at a distance of $\lambda x$ from the ice end A, find the value of $\lambda$. [Neglect any heat loss to the surrounding.]

An ideal gas is expanding such that $PT^2=$ constant. The coefficient of volume expansion of the gas is

Column I gives some devices and Column II gives some processes on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.