Question 1

The heat current is written as ΔtΔQ​ . Why don't we write dtdQ​ ?

Accepted Answer

The amount of heat crossing through any cross-section of a slab in time Δt  is called heat current.It is written as ΔtΔQ​  and not ΔtΔQ​   as complete derivative . This is because the amount of heat crossing through any cross section is a function of many variables like temperature difference, area of cross-section, etc. So, we cannot write it as a complete derivative with respect to time.

Question 2

Does a body at 20°C radiate in a room, where the room temperature is 30°C? If yes, why does its temperature not fall further?

Accepted Answer

Yes, the body will radiate. However, its temperature will not fall down with time because as the temperature of the surroundings is greater than the temperature of the body so, its rate of absorption will be greater than its rate of emission.

Question 3

Why does blowing over a spoonful of hot tea cools it? Does evaporation play a role? Does radiation play a role?

Accepted Answer

Here, major role is played by convection. When we blow air over a spoonful of hot tea, the air coming from our mouth has less temperature than the air above the tea. Since hot air has less density, it rises up and cool air goes down. In this way, the tea cools down.We know that any hot body radiates. So, the spoonful of tea will also radiate and as the temperature of the surrounding is less then the tea, the tea will cool down with time. Evaporation is also involved in this. On blowing over the hot tea, rate of evaporation increases and the cools down.

Question 4

On a hot summer day we want to cool our room by opening the refrigerator door and closing all the windows and doors. Will the process work?

Accepted Answer

No. When the door of the refrigerator is left open in a closed room, the heat given out by the refrigerator to the room will be more than that taken from the room. Therefore, instead of decreasing, the temperature of the room will increase at a slower rate.

Question 5

On a cold winter night you are asked to sit on a chair. Would you like to choose a metal chair or a wooden chair? Both are kept in the same lawn and are at the same temperature.

Accepted Answer

We will prefer to seat on a wooden chair because as the conductivity of wood is poorer than that of metal, heat flow from our body to the chair will be less in case of a wooden chair.

Question 6

Two identical metal balls one at T1​  = 300 K and the other at T2​  = 600 K are kept at a distance of 1 m in a vacuum. Will the temperatures equalise by radiation? Will the rate of heat gained by the colder sphere be proportional to t24​−t14​  as may be expected from the Stefan's law?

Accepted Answer

Yes, the temperature of the balls can be equalised by radiation. This is because both the spheres will emit radiations in all the directions at different rates.The ball kept at the temperature of 300 K will gain some thermal energy by the radiation emitted by the ball kept at the temperature of 600 K. Also, it losses energy by radiation.Similarly, the ball kept at the temperature of 600 K will gain some thermal energy by the radiation emitted by the ball kept at the temperature of 600 K. Also, it losses energy by radiation.A time comes when the temperature of both the bodies becomes equal.Yes, the rate of heat gained by the colder sphere is proportional to t24​−t14​ .

Question 7

An ordinary electric fan does not cool the air, still it gives comfort in summer. Explain

Accepted Answer

An ordinary electric fan does not cool the air, still it gives comfort in summer because it circulates the air present in the room. Due to this, evaporation takes place and we feel cooler.

Question 8

The temperature of the atmosphere at a high altitude is around 500°C. Yet an animal there would freeze to death and not boil. Explain.

Accepted Answer

The temperature of the atmosphere at a high altitude is around 500°C, but density of air molecule is extremely low at this height. So, very less molecules of air collide with the body of the animal and transfer very less amount of heat. That is why the animal present there would freeze to death instead boiling.

Question 9

Standing in the sun is more pleasant on a cold winter day than standing in shade. Is the temperature of air in the sun considerably higher than that of the air in shade?

Accepted Answer

The heat coming from the sun to us is through the radiation. On colder winter days, when we stand in shade, we do not get the heat of the sun from the radiation. Though we feel cool in the shade, the temperature of the air in shady as well as non-shady regions is the same.

Question 10

Cloudy nights are warmer than the nights with clean sky. Explain.

Accepted Answer

During night, the earth's surface radiates infrared radiation of larger wavelength. Gas molecules in the air absorb some of this energy and radiate energy of their own in all directions. Also, water molecules, like the vapour that makes the clouds, absorb more frequencies of infrared energy than clear air does.Both these factors contribute to the fact that clouds radiate more heat in all directions (including the earth) than clear air does. In turn, this makes the overall temperature on the earth warmer when there is a cloud cover. The heat energy radiated by the earth is reflected back to earth. Due to this, cloudy nights are warmer than the nights with clean sky.

Question 11

Why is a white dress more comfortable than a dark dress in summer?

Accepted Answer

A white colour dress reflects almost all the radiations falling on it. So, it does not absorb any heat from the sunlight and we feel more comfortable in it. On the other hand, a dark colour dress absorbs maximum radiation falling on it. So, we feel hot in a dark coloured dress during summers.

Question 12

The thermal conductivity of a rod depends on:

Accepted Answer

(d) Material of the rod.The thermal conductivity of a rod depends only on the material of the rod. For example, metals are much better conductors than non-metals because metals have large number of free electron that can move freely anywhere in the body of the metal and carry thermal energy from one place to other. Also, 2 copper rods having different lengths and areas of cross-section have same thermal conductivity that depends only on the number of free electrons in copper.

Question 13

In a room containing air, heat can go from one place to another:

Accepted Answer

(d) By all the three modes.In conduction, heat is transferred from one place to other by vibration of the molecules. In this process, the average position of a molecule does not change. Hence, there is no mass movement of matter.In convection, heat is transferred from one place to other by actual motion of particles of the medium. When water is heated, hot water moves upwards and cool water moves downwards.In radiation process, transfer of heat does not require any material medium.For a room containing air, heat can be transferred via radiation (no medium required) and convection (by the movement of air molecules) and by conduction (due to collision of hot air molecules with other molecules).

Question 14

A solid at temperature T1​  is kept in an evacuated chamber at temperature T2​>T1​ . The rate of increase of temperature of the body is proportional to:

Accepted Answer

(d) T24​−T14​ .From Stefan-Boltzmann law, the energy of thermal radiation emitted per unit time by a blackbody of surface area A is given by u=σAT4 Here,  σσ  is Stefan-Boltzmann constant.Since the temperature of the solid is less than the surroundings, the temperature of the solid will increase with time until it reaches equilibrium with the surroundings. The rate of emission from the solid will be proportional to T14​  and rate of emission from the surroundings will be proportional to T24​ .So, the net rate of increase in temperature will be proportional to T24​−T14​ .

Question 15

The thermal radiation emitted by a body is proportional to Tn​  where T is its absolute temperature. The value of n is exactly 4 for:

Accepted Answer

(b) All the bodies.From Stefan-Boltzmann law, the energy of the thermal radiation emitted per unit time by a blackbody of surface area A is given by u=σAT4  Here , σ is Stefan-Boltzmann constant.This law holds true for all the bodies.

Question 16

Two bodies A and B having equal surface areas are maintained at temperature 10°C and 20°C. The thermal radiation emitted in a given time by A and B are in the ratio:

Accepted Answer

(a) 1 : 1.15.From Stefan-Boltzmann law, energy of the thermal radiation emitted per unit time by a blackbody of surface area A  is given byu=σAT4 Here, σ  is Stefan-Boltzmann constant.The thermal radiation emitted in a given time by A and B will be in the ratiouB​uA​​=TB4​TA4​​  
uB​uA​​=(273+20)4(273+10)4​

uB​uA​​=1.151​

Question 17

One end of a metal rod is kept in a furnace. In steady state, the temperature of the rod:

Accepted Answer

(d) Is non uniform.In steady state, the temperature of the rod is nonuniform maximum at the end near the furnace and minimum at the end that is away from the furnace.

Question 18

Newton's law of cooling is a special case of:

Accepted Answer

(c)Stefan's law.From Stefan-Boltzman's law, the energy of the thermal radiation emitted per unit time by a blackbody of surface area A is given by, u=σAT4 Where σ  is Stefan's constant.Suppose a body at temperature T is kept in a room at temperature T0​. According to Stefan's law, energy of the thermal radiation emitted by the body per unit time is u=eσAT4 Here, e is the emissivity of the body.The energy absorbed per unit time by the body is (due to the radiation emitted by the walls of the room Δu=eσAT04​. Thus, the net loss of thermal energy per unit time is Δu=eσA(T4−T04​) ...(i) Newton law of cooling is given by(dT)/(dt)=−bA(T−T0​) This can be obtained from equation (i) by considering the temperature difference to be small and doing the binomial expansion.

Question 19

A hot liquid is kept in a big room. Its temperature is plotted as a function of time. Which of the following curves may represent the plot?

Accepted Answer

(a)When a hot liquid is kept in a big room, the liquid will loose its temperature with time. The thermal energy emitted by the liquid will be gained by the walls of the room. As the room is big, we can assume that the temperature difference between the room and the liquid is large. From Stephen's law, the liquid emits thermal energy in proportion to T4 , where T is the initial temperature of the liquid.As the temperature decreases, the rate of loss of thermal energy will also decrease. So, the slope of the curve will also decrease.Therefore, the plot of temperature with time is best represented by the curve (a).

Question 20

A hot liquid is kept in a big room. The logarithm of the numerical value of the temperature difference between the liquid and the room is plotted against time. The plot will be very nearly:

Accepted Answer

(a) A straight line.When a hot liquid is kept in a big room, then the liquid will loose temperature with time. The thermal energy emitted by the liquid will be gained by the walls of the room. As the room is big, we can assume that the temperature difference between the room and the liquid is large. From Stephen's law, the liquid emits thermal energy in proportion to T4 , where T is the initial temperature of the liquid. As the temperature decreases, the rate of loss will also decrease. So, the slope of the curve will also decrease. Finally, at equilibrium, the temperature of the room will become equal to the new temperature of the liquid. So, in steady state, the difference between the temperatures of the two will become zero.A graph is plotted between the logarithm of the numerical value of the temperature difference between the liquid and the room is plotted against time. The logarithm converts the fourth power dependence into a linear dependence with some coefficient (property of log). So, the plot satisfying all the above properties will be a straight line.

Chapter 6 : Heat Transfer