The total radiant energy per unit area per unit time, normal to the direction of incidence, received at a distance R from the centre of a star of radius r,whose outer surface radiates as a black body at a temperature TK is given by 

(a) $\sigma r^2{T}^4/R^2$                                       (b) $\sigma r^2{T}^4/4{\mathrm{\pi r}}^2$

(c) $\sigma r^4{T}^4/r^4$                                        (d) $4\mathrm{\pi } \sigma r^2{T}^4/R^2$

(where $\sigma$ is Stefan's constant)

A black body at $227°C$ radiates heat at the rate of 7 cal $c{m}^{-2}{s}^{-1}.$ At a temperature of $727°C,$ the rate of heat radiated in the same units will be 

On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are $39°W$ and $239°W$ respectively. What will be the temperature on the new scale, corresponding to a temperature of $39°C$ on the Celsius scale?

To keep constant time, watches are fitted with balance wheel made of -

A metal bar of length L and area of cross-section A is clamped between two rigid supports. For the material of the rod, its Young’s modulus is Y and the coefficient of linear expansion is $\alpha$. If the temperature of the rod is increased by $∆t°C$, the force exerted by the rod on the supports will be:

The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume ? The volume elasticity of the cube is  $\beta$ and the coefficient of volume expansion is $\alpha$ -

Under steady state, the temperature of a body 

The coefficient of thermal conductivity depends upon

When two ends of a rod wrapped with cotton are maintained at different temperatures and, after some time, every point of the rod attains a constant temperature, then

The ratio of thermal conductivity of two rods of different material is 5 : 4. The two rods of same area of cross-section and same thermal resistance will have the lengths in the ratio 

In variable state, the rate of flow of heat is controlled by

The dimensions of thermal resistance are

Two walls of thicknesses ${\mathrm{d}}_1$ and ${\mathrm{d}}_2$ and thermal conductivities ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are in contact. In the steady state, if the temperatures at the outer surfaces  are ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, the temperature at the common wall is  -

A slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio 1 : 4. If the free face of brass is at 100°C and that of copper at 0°C, the temperature of interface is

Two thin blankets keep more hotness than one blanket of thickness equal to these two. The reason is

Ice formed over lakes has

Taking into account the radiation that a human body emits which of the following statements is true?

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

Wires A and B have identical lengths and have circular cross-sections. The radius of A is twice the radius of B i.e. ${\mathrm{r}}_{\mathrm{A}}=2{\mathrm{r}}_{\mathrm{B}}$ . For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by

Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of conductivity of each plate are 2 and 3 respectively, then the conductivity of the composite plate will be:

The coefficients of thermal conductivity of copper, mercury and glass are respectively ${\mathrm{K}}_{\mathrm{c}}$, ${\mathrm{K}}_{\mathrm{m}}$ and ${\mathrm{K}}_{\mathrm{g}}$ such that ${\mathrm{K}}_{\mathrm{c}}>{\mathrm{K}}_{\mathrm{m}}>{\mathrm{K}}_{\mathrm{g}}$. If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are ${\mathrm{X}}_{\mathrm{c}}$, ${\mathrm{X}}_{\mathrm{m}}$ and ${\mathrm{X}}_{\mathrm{g}}$, then 

If two metallic plates of equal thicknesses and thermal conductivities ${\mathrm{K}}_1$ and ${\mathrm{K}}_2$ are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

The quantity of heat which crosses unit area of a metal plate during conduction depends upon

Two spheres of different materials one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the time taken for complete melting of ice in the larger sphere is 25 minutes and that for smaller sphere 16 minutes, the ratio of thermal conductivities of the materials of larger sphere to the smaller sphere is 

Mud houses are cooler in the summer and warmer in the winter because:

The temperature of the hot and cold ends of a 20 cm long rod in a thermal steady state is at 100^oC and 20^oC respectively. The temperature at the centre of the rod will be:

Two bars of thermal conductivities K and 3K and lengths 1 cm and 2 cm respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is 0$°\mathrm{C}$ and 100$°\mathrm{C}$ respectively (see figure), then the temperature $\varphi$ of the interface is

A heat flux of 4000 J/s is to be passed through a copper rod of length 10 cm and area of cross-section 100 ${\mathrm{cm}}^2$. The thermal conductivity of copper is 400 W/m$°\mathrm{C}$. The two ends of this rod must be kept at a temperature difference of 

On a cold morning, a metal surface will feel colder to touch than a wooden surface because 

At a common temperature, a block of wood and a block of metal feel equally cold or hot. The temperatures of block of wood and block of metal are