Newton's Law of Cooling

Two hot bodies $B_1$ and $B_2$ have temperature $100^\circ$C and $80^\circ$C respectively at $t = 0$. The temperature of the surroundings is $40^\circ$C. The ratio of the respective rates of cooling $R_1$ and $R_2$ of these two bodies at $t = 0$ will be

A body cools from a temperature $3\theta$ to $2\theta$ in 10 minute. The room temperature is $\theta$. The temperature of the body at the end of the next 10 minute is '$x$'. Assuming that Newton's law of cooling is applicable, the value of '$x$' will be

A bowl filled with very hot water cools from $98^\circ$C to $86^\circ$C in 2 minutes when the room temperature is $22^\circ$C. How long it will take to cool from $75^\circ$C to $69^\circ$C?

An ordinary body cools from $4\theta$ to $3\theta$ in 't' minutes. The temperature of the body after next 't' minutes is (Assume Newton's law of cooling and room temperature as $\theta$)

A body cools in $7$ minutes from $60^\circ$ C to $40^\circ$ C. What time (in minutes) does it take to cool from $40^\circ$C to $28^\circ$ C, if its surrounding temperature is $10^\circ$C? (Newton's law of cooling holds good)

A body cools from $80^\circ\text{C}$ to $50^\circ\text{C}$ in 5 min. In the next time of ' t ' in, the body continues to cool from $50^\circ\text{C}$ to $30^\circ\text{C}$. The total time taken by the body to cool from $80^\circ\text{C}$ to $30^\circ\text{C}$ is [The temperature of the surroundings is $20^\circ\text{C}$.]

Hot water cools from $80^\circ\text{C}$ to $60^\circ\text{C}$ in 1 minutes. In cooling from $60^\circ\text{C}$ to $50^\circ\text{C}$ it will take (room temperature $= 30^\circ\text{C}$)

A metal sphere cools at a rate of $1.5^\circ\text{C/min}$ when its temperature is $80^\circ\text{C}$. When the temperature of the sphere is $40^\circ\text{C}$, its rate of cooling is $0.3^\circ\text{C/min}$. The temperature of the surrounding $(\theta_0)$ is

A body cools from $60^\circ\text{C}$ to $40^\circ\text{C}$ in 6 minutes. After next 6 minutes its temperature will be (Temperature of the surroundings is $10^\circ\text{C}$)

A cup of coffee cools from 90°C to 80°C in t minutes when the room temperature is 20°C. The time taken by the similar cup of coffee to cool from 80°C to 60°C at the same room temperature is:

The temperature of a body in air falls from $40^\circ\text{C}$ to $24^\circ\text{C}$ in 4 minutes. The temperature of the air is $16^\circ\text{C}$. The temperature of the body in the next 4 minutes will be:

A calorimeter contains 10 g of water at $20^\circ\text{C}$. The temperature fall to $15^\circ\text{C}$ in 10 min. When calorimeter contains 20 g of water at $20^\circ\text{C}$, it takes 15 min. for the temperature to become $15^\circ\text{C}$. The water equivalent at the calorimeter is

A bucket full of hot water is kept in a room. If it cools from $75^\circ\text{C}$ to $70^\circ\text{C}$ in $t_1$ minutes, from $70^\circ\text{C}$ to $65^\circ\text{C}$ in $t_2$ minutes and $65^\circ\text{C}$ to $60^\circ\text{C}$ in $t_3$ minutes, then

An ordinary body cools from ' $4\theta'$ ' to ' $3\theta'$ ' in ' t ' minutes. The temperature of that body after next 't' minutes is (Assume Newton's law of cooling and room temperature is $\theta$)

The temperature of a liquid falls from 365 K to 359 K in 3 minutes. The time during which temperature of this liquid falls from 342 K to 338 K is [Let the room temperature be 296 K ]

A metal rod cools at the rate of $4^\circ\text{C/min}$ when its temperature is $90^\circ\text{C}$ and the rate of $1^\circ\text{C/m}$in when its temperature is $30^\circ\text{C}$. The temperature of the surrounding is

Read the following statements:

A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice.

B. Two bodies $P$ and $Q$ having equal surface areas are maintained at temperature $10^\circ\text{C}$ and $20^\circ\text{C}$. The thermal radiation emitted in a given time by $P$ and $Q$ are in the ratio $1 : 1.15$. C. A Carnot Engine working between $100\text{ K}$ and $400\text{ K}$ has an efficiency of $75\%$.

D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.

Choose the correct answer from the options given below:

A metal sphere cools at the rate of $1.5^\circ\text{C/min}$ when its temperature is $80^\circ\text{C}$. At what rate will it cool when its temperature falls to $50^\circ\text{C}$. [Temperature of surrounding is $30^\circ\text{C}$]

A cup of coffee cools from 90$^\circ$ C to 80$^\circ$C in t minutes, when the room temperature is 20$^\circ$ C. The time taken by a similar cup of coffee to cool from 80$^\circ$C to 60$^\circ$C at a room temperature same at 20$^\circ$C is:

Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8 × 102 kg/m3 and specific heat of 2000 J kg–1 K–1 while liquid in B has density of 103 kg m–3 and specific heat of 4000 J kg–1 K–1. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)