A black body at a temperature of 227$°\mathrm{C}$ radiates heat energy at the rate of 5 $\mathrm{cal}/{\mathrm{cm}}^2-\sec$. At a temperature of $727°\mathrm{C}$, the rate of heat radiated per unit area in $\mathrm{cal}/{\mathrm{cm}}^2$ will be 
(1) 80                     

(2) 160

(3) 250                   

(4) 500

The area of a hole of heat furnace is ${10}^{-4} {\mathrm{m}}^2$. It radiates $1.58\times {10}^5$ calories of heat per hour. If the emissivity of the furnace is 0.80, then its temperature is
(1) 1500 K           

(2) 2000 K

(3) 2500 K           

(4) 3000 K

Two spherical black bodies of radii ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ and with surface temperature ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ respectively radiate the same power. Then the ratio of ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ will be

(a) ${\left(\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}\right)}^2$                (b) ${\left(\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}\right)}^4$
(c) ${\left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right)}^2$                (d) ${\left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right)}^4$

If the sun’s surface radiates heat at \(6.3\times 10^{7}~\text{Wm}^{-2}\) ${\mathrm{}}^{}$then the temperature of the sun, assuming it to be a black body, will be:
\(\left(\sigma = 5.7\times 10^{-8}~\text{Wm}^{-2}\text{K}^{-4}\right)\)
1. \(5.8\times 10^{3}~\text{K}\)
2. \(8.5\times 10^{3}~\text{K}\)
3. \(3.5\times 10^{8}~\text{K}\)
4. \(5.3\times 10^{8}~\text{K}\)

Two identical objects A and B are at temperatures ${\mathrm{T}}_{\mathrm{A}}$ and ${\mathrm{T}}_{\mathrm{B}}$ respectively. Both objects are placed in a room with perfectly absorbing walls maintained at temperatures T(${\mathrm{T}}_{\mathrm{A}}$>T>${\mathrm{T}}_{\mathrm{B}}$). The objects A and B attain temperature T eventually. Which one of the following is the correct statement?

(1) ‘A’ only emits radiations while B only absorbs them until both attain temperature

(2) A loses more radiations than it absorbs while B absorbs more radiations than it emits until temperature T is attained

(3) Both A and B only absorb radiations until they attain temperature T

(4) Both A and B only emit radiations until they attain temperature T

In Newton's experiment of cooling, the water equivalent of two similar calorimeters is 10 gm each. They are filled with 350 gm of water and 300 gm of a liquid (equal volumes) separately. The time taken by water and liquid to cool from 70°C to 60°C is 3 min and 95 sec respectively. The specific heat of the liquid will be
(1) 0.3 Cal/gm $\times$°C                       

(2) 0.5 Cal/gm $\times$°C

(3) 0.6 Cal/gm $\times$°C                       

(4) 0.8 Cal/gm $\times$°C

Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The points A and B are maintained at different temperature. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross section of the straight rod in a given time is 

(1) 2 : $\mathrm{\pi }$ 

(2) 1 : 2

(3) $\mathrm{\pi }$ : 2

(4) 3 : 2

Three rods of identical area of cross-section and made from the same metal form the sides of an isosceles triangle ABC, which is right-angled at B. The points A and B are maintained at temperatures T and $\sqrt{2}\mathrm{T}$ respectively. In the steady state, the temperature of point C is ${\mathrm{T}}_{\mathrm{C}}$. Assuming that only heat conduction takes place, $\frac{{\mathrm{T}}_{\mathrm{C}}}{\mathrm{T}}$ is equal to:
1. $\frac{1}{\left(\sqrt{2}+1\right)}$
2. $\frac{3}{\left(\sqrt{2}+1\right)}$
3. $\frac{1}{2\left(\sqrt{2}-1\right)}$                  
4. $\frac{1}{\sqrt{3}\left(\sqrt{2}-1\right)}$

The only possibility of heat flow in a thermos flask is through its cork which is 75 ${\mathrm{cm}}^2$ in area and 5 cm thick. Its thermal conductivity is 0.0075 cal/cmsec$°\mathrm{C}$. The outside temperature is 40$°\mathrm{C}$ and latent heat of ice is 80 cal ${\mathrm{g}}^{-1}$. Time taken by 500 g of ice at 0$°\mathrm{C}$ in the flask to melt into water at 0$°\mathrm{C}$ is -

(a) 2.47 hr
(b) 4.27 hr
(c) 7.42 hr
(d) 4.72 hr

Two identical conducting rods are first connected independently to two vessels, one containing water at 100$°\mathrm{C}$ and the other containing ice at 0$°\mathrm{C}$. In the second case, the rods are joined end to end and connected to the same vessels. Let ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ g / s be the rate of melting of ice in two cases respectively. The ratio of ${\mathrm{q}}_1$/${\mathrm{q}}_2$ is

(a) $\frac{1}{2}$                 (b) $\frac{2}{1}$
(c) $\frac{4}{1}$                 (d) $\frac{1}{4}$