A bucket full of hot water cools from 75$°\mathrm{C}$ to 70$°\mathrm{C}$ in time ${\mathrm{T}}_1$, from 70$°\mathrm{C}$ to 65$°\mathrm{C}$ in time ${\mathrm{T}}_2$  and from 65$°\mathrm{C}$ to 60$°\mathrm{C}$ in time ${\mathrm{T}}_3$, then 
(1) ${\mathrm{T}}_1={\mathrm{T}}_2={\mathrm{T}}_3$              

(2) ${\mathrm{T}}_1>{\mathrm{T}}_2>{\mathrm{T}}_3$

(3) ${\mathrm{T}}_1<{\mathrm{T}}_2<{\mathrm{T}}_3$               

(4) ${\mathrm{T}}_1>{\mathrm{T}}_2<{\mathrm{T}}_3$

Consider two hot bodies, ${\mathrm{B}}_1$ and ${\mathrm{B}}_2$ which have temperatures of \(100^{\circ}\mathrm{C}\)$\mathrm{}$ and \(80^{\circ}\mathrm{C}\)$\mathrm{}$ respectively at t=0. The temperature of the surroundings is \(40^{\circ}\mathrm{C}\)$\mathrm{}$. The ratio of the respective rates of cooling ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ of these two bodies at t = 0 will be:
1. ${\mathrm{R}}_1:{\mathrm{R}}_2=3:2$
2. ${\mathrm{R}}_1:{\mathrm{R}}_2=5:4$
3. ${\mathrm{R}}_1:{\mathrm{R}}_2=2:3$
4. ${\mathrm{R}}_1:{\mathrm{R}}_2=4:5$

Newton's law of cooling is a special case of
(1) Stefan's law           

(2) Kirchhoff's law

(3) Wien's law             

(4) Planck's law

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

Which of the following statements is true/correct ?

(1) During clear nights, the temperature rises steadily upward near the ground level

(2) Newton's law of cooling, an approximate form of Stefan's law, is valid only for natural convection

(3) The total energy emitted by a black body per unit time per unit area is proportional to the square of its temperature in the Kelvin scale

(4) Two spheres of the same material have radii 1m and 4m and temperatures 4000 K and 2000 K respectively. The energy radiated per second by the first sphere is greater than that radiated per second by the second sphere

The rates of cooling of two different liquids put in exactly similar calorimeters and kept in identical surroundings are the same if 

(1) The masses of the liquids are equal

(2) Equal masses of the liquids at the same temperature are taken

(3) Different volumes of the liquids at the same temperature are taken

(4) Equal volumes of the liquids at the same temperature are taken

The temperature of a liquid drops from 365 K to 361 K in 2 minutes. Find the time during which temperature of the liquid drops from 344 K to 342 K . Temperature of room is 293 K
(a) 84 sec                        (b) 72 sec
(c) 66 sec                        (d) 60 sec

Newton’s law of cooling, holds good only if the temperature difference between the body and the surroundings is
(1) Less than 10$°\mathrm{C}$      

(2) More than 10$°\mathrm{C}$

(3) Less than 100$°\mathrm{C}$     

(4) More than 100$°\mathrm{C}$

The temperature of a body falls from 50$°\mathrm{C}$ to 40$°\mathrm{C}$ in 10 minutes. If the temperature of the surroundings is 20$°\mathrm{C}$, then temperature of the body after another 10 minutes will be- 
(1) 36.6$°\mathrm{C}$           

(2) 33.3$°\mathrm{C}$

(3) 35$°\mathrm{C}$               

(4) 30$°\mathrm{C}$

A body takes \(5\) minutes to cool from \(90^{\circ}\text{C}\)$\mathrm{}$ to \(60^{\circ}\text{C}\)$\mathrm{}$. If the temperature of the surroundings is \(20^{\circ}\text{C}\)$\mathrm{}$, the time taken by it to cool from \(60^{\circ}\text{C}\)$\mathrm{}$ to \(30^{\circ}\text{C}\)$\mathrm{}$ will be:
1. \(5~\text{min}\)
2. \(8~\text{min}\)
3. \(11~\text{min}\)
4. \(12~\text{min}\)