A liquid takes 5 minutes to cool from 80 ° C to 50 ° C . How much time will it take to cool from 60 ° C to 30 ° C ? The temperature of the surroundings is 20 ° C .

Newton's law of cooling states that the rate of decrease in temperature of a body due to radiation is proportional to the difference in temperature between the body and its surroundings. Using newton's law of cooling by the average method. d T d t = - k T body - T out where k is cooling constant which depends on the nature of material and its specific heat capacity. When the body cools from one temperature to another. The temperature of the body in the given formula will be taken as the average of initial and final temperatures. From the given question, in scenario 1 , Initial temperature, T i = 80 ° C Final temperature, T f = 50 ° C The amount of cooling is measured as, ∆ T = 50 - 80 = - 30 ° C It cools over a period of t = 5 min , So, we can calculate k by, - 30 5 = - k 80 + 50 2 - 20 ⇒ - 6 = - k ( 45 ) ⇒ k = 2 15 Substituting this in the second case where the temperature decreases from 60 to 30 is, - 30 t = - k 60 + 30 2 - 20 ⇒ 30 t = 2 15 × 25 ⇒ 30 × 15 2 × 25 = t t = 9 min .

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A rod $C D$ of thermal resistance $5 K W^{- 1}$ is joined in the middle to an identical rod $A B$ as shown in the figure. The ends $A$ , $B$ and $D$ are maintained at $100 ° C$ , $0 ° C$ and $25 ° C$ , respectively. Find the heat current in $C D$ .

Important Questions on Calorimetry and Heat Transfer

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JEE Advanced

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Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 6 - Calorimetry and Heat Transfer>INTRODUCTORY EXERCISE 22.2>Q 5

A liquid takes

5 minutes

to cool from

80 ° C

50 ° C

. How much time will it take to cool from

60 ° C

30 ° C

? The temperature of the surroundings is

20 ° C

EASY

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Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 6 - Calorimetry and Heat Transfer>Exercises>Q 9

For an enclosure maintained at

2000 K

, the maximum radiation occurs at wavelength

λ_{m}

. If the temperature is raised to

3000 K

, the peak will shift to

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JEE Advanced

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Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 6 - Calorimetry and Heat Transfer>Exercises>Q 10

A substance cools from

75 ° C

70 ° C

T_{1} minute

, from

70 ° C

65 ° C

T_{2} minute

and from

65 ° C

60 ° C

T_{3} minute

, then

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Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 6 - Calorimetry and Heat Transfer>Exercises>Q 1

Two liquids are at temperatures

20 ° C

and

40 ° C

. When the same mass of both of them is mixed, the temperature of the mixture is

32 ° C

. What is the ratio of their specific heats?

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Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 6 - Calorimetry and Heat Transfer>Exercises>Q 2

The specific heat of metal at low temperatures varies according to

S = a T^{3}

where

a

is constant and

T

is the absolute temperature. The heat energy needed to raise the unit mass of the metal from temperature

T = 1 K

T = 2 K

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Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 6 - Calorimetry and Heat Transfer>Exercises>Q 3

The intensity of radiation emitted by the sun has its maximum value at a wavelength of

510 nm

and that emitted by the North star has the maximum value at

350 nm

. If these stars behave like black bodies, then the ratio of the surface temperatures of the sun and the north star is

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Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 6 - Calorimetry and Heat Transfer>Exercises>Q 4

The solid material is supplied heat at a constant rate. The temperature of the material is changing with heat input as shown in the figure. What does the slope of $D E$ represent?

Question Image

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Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 6 - Calorimetry and Heat Transfer>Exercises>Q 5

Two ends of rods of length

L

and radius

R

of the same material are kept at the same temperature. Which of the following rods conducts the maximum heat?

A rod CD of thermal resistance 5 K W-1 is joined in the middle to an identical rod AB as shown in the figure. The ends A, B and D are maintained at 100 °C, 0 °C and 25 °C, respectively. Find the heat current in CD.

Important Questions on Calorimetry and Heat Transfer

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A rod $C D$ of thermal resistance $5 K W^{- 1}$ is joined in the middle to an identical rod $A B$ as shown in the figure. The ends $A$ , $B$ and $D$ are maintained at $100 ° C$ , $0 ° C$ and $25 ° C$ , respectively. Find the heat current in $C D$ .