The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively are ${\mathrm{T}}_2$ and ${\mathrm{T}}_1$ (${\mathrm{T}}_2$ > ${\mathrm{T}}_1$). The rate of heat transfer through the slab, in a steady state is $\left(\frac{\mathrm{A}\left({\mathrm{T}}_2-{\mathrm{T}}_1\right)\mathrm{K}}{\mathrm{x}}\right)\mathrm{f}$, with f which equals to -

(a) 1
(b) $\frac{1}{2}$
(c) $\frac{2}{3}$
(d) $\frac{1}{3}$

The figure shows a system of two concentric spheres of radii ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ and kept at temperatures ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to -

(a) $\frac{{\mathrm{r}}_1{\mathrm{r}}_2}{\left({\mathrm{r}}_1-{\mathrm{r}}_2\right)}$
(b) $\left({\mathrm{r}}_1-{\mathrm{r}}_2\right)$
(c) $\left({\mathrm{r}}_1-{\mathrm{r}}_2\right)\left({\mathrm{r}}_1{\mathrm{r}}_2\right)$
(d) In $\left(\frac{{\mathrm{r}}_2}{{\mathrm{r}}_1}\right)$

The graph shown in the adjacent diagram, represents the variation of temperature (T) of two bodies, x and y having same surface area, with time (t) due to the emission of radiation. Find the correct relation between the emissivity (e) and absorptivity (a) of the two bodies .

The plots of intensity versus wavelength for three black bodies at temperatures ${\mathrm{T}}_1$, ${\mathrm{T}}_2$ and ${\mathrm{T}}_3$ respectively are as shown. Their temperature are such that

(a) ${\mathrm{T}}_1$>${\mathrm{T}}_2$>${\mathrm{T}}_3$
(b)  ${\mathrm{T}}_1$>${\mathrm{T}}_3$>${\mathrm{T}}_2$
(c) ${\mathrm{T}}_2$ >${\mathrm{T}}_3$ >${\mathrm{T}}_1$
(d) ${\mathrm{T}}_3$>${\mathrm{T}}_2$ > ${\mathrm{T}}_1$

The adjoining diagram shows the spectral energy density distribution ${\mathrm{E}}_{\mathrm{\lambda }}$ of a black body at two different temperatures. If the areas under the curves are in the ratio 16 : 1, the value of temperature T is 

Variation of radiant energy emitted by sun, filament of tungsten lamp and welding arc as a function of its wavelength is shown in figure. Which of the following option is the correct match?

Shown below are the black body radiation curves at temperatures ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ (${\mathrm{T}}_2$>${\mathrm{T}}_1$). Which of the following plots is correct ?

The spectrum of a black body at two temperatures 27$°\mathrm{C}$ and 327$°\mathrm{C}$ is shown in the figure. Let ${\mathrm{A}}_1$ and ${\mathrm{A}}_2$ be the areas under the two curves respectively. The value of $\frac{{\mathrm{A}}_2}{{\mathrm{A}}_1}$ is

A block of metal is heated to a temperature much higher than the room temperature and allowed to cool in a room free from air currents. Which of the following curves correctly represents the rate of cooling?

The energy distribution E with the wavelength $\left(\mathrm{\lambda }\right)$ for the black body radiation at temperature T Kelvin is shown in the figure. As the temperature is increased the maxima will:
     

For a small temperature difference between the body and the surroundings the relation between the rate of loss heat R and the temperature of the body $\theta$is depicted by -

Heat is flowing through a conductor of length l from x = 0 to x = l. If its thermal resistance per unit length is uniform, which of the following graphs is correct ?

Two balls of the same material and same surface finish have their diameters in the ratio 1:2. They are heated to the same temperature and are left in a room to cool by radiation, then the initial rate of loss of heat:

Radius of a conductor increases uniformly from left end to right end as shown in fig.

Material of the conductor is isotropic and its curved surface is thermally isolated from surrounding. Its ends are maintained at temperatures ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ (${\mathrm{T}}_1$ > ${\mathrm{T}}_2$): If in steady state, heat flow rate is equal to H, then which of the following graphs is correct 

Which of the following graphs correctly represents the relation between \(ln~E\) and \(ln~T\) where E is the amount of radiation emitted per unit time from a unit area of a body and T is the absolute temperature?\(\left (Take~\sigma =5.67\times 10^{-8} ~W~m^{-2}~K^{-4}~and~0<\epsilon <1 \right )\)

A hollow copper sphere S and a hollow copper cube C, both of negligible thin walls of same area, are filled with water at 90°C and allowed to cool in the same environment. The graph that correctly represents their cooling is -

In the figure, the distribution of energy density of the radiation emitted by a black body at a given temperature is shown. The possible temperature of the black body is

Which of the following is the ${\mathrm{v}}_{\mathrm{m}}$ v/s  T graph for a perfectly black body (${\mathrm{v}}_{\mathrm{m}}$ = frequency of peak radiation) ?

The vapour of a substance behaves as a gas :

The temperature below which gas should be cooled, before it can be liquified by pressure only is termed as :

The change in volume V with respect to an increase in pressure P has been shown in the figure for a non-ideal gas at four different temperatures ${\mathrm{T}}_1, {\mathrm{T}}_2,{\mathrm{T}}_3$ and ${\mathrm{T}}_4$ . The critical temperature of the gas is

In the adjoining figure, various isothermals are shown for a real gas. Then

At what temperature do both the Centigrade and Fahrenheit thermometers show the same reading

The temperature of substance increases by 27°C this increases is equal to (in kelvin)

The temperature of a substance increases by $27°\mathrm{C}$. On the Kelvin scale, this increase is equal to

Two rods A and B of different materials are welded together as shown in the figure. Their thermal conductivities are K₁ and K₂. The thermal conductivity of the composite rod will be:

The power radiated by a black body is P and it radiates maximum energy at wavelength ${\lambda }_0$. If the temperature of the black body is now changed so that it radiates maximum energy at the wavelength $\frac{3}{4}{\lambda }_0$. The power radiated by it becomes nP. The value of n is: