Answers to Problems on Heat Transfer HC Verma's Questions for Short Answer

Q#1

The heat current is written as ΔQ/Δt why don't we write dQ/dt? 

Answer:  

In dQ/dt, dQ is the change corresponding to dt which is an infinitesimal time that means Δt →0. It means Δt is not zero but very very near to zero, as much near as you can go. Obviously, you can not measure dt. So to define the heat current a very small but measurable time Δt is taken and the corresponding flow of heat ΔQ is measured and the heat current is defined as ΔQ/Δt. 

Q#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? 

Answer:  

Yes, because all bodies radiate thermal radiation at all temperatures.

The temperature of the body does not fall further because simultaneously it absorbs a part of the heat radiation falling on it from the surrounding bodies which are at a higher temperature. 

Q#3

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

Answer:  

Yes both evaporation and radiation play a role. While blowing increases the evaporation and the evaporation takes heat energy from the liquid itself. So it cools faster.

Radiation plays a role but does not depend on blowing. Here, in a spoon, the area of the liquid is comparatively greater compared to the volume of the liquid. The radiation is directly proportional to the area.

Q#4

Together these phenomena cool the tea in the spoon.  

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? 

Answer:  

A refrigerator does not cool inside directly using electric current but it uses a compressor to bring out the heat from inside and this heat is radiated into the room using radiators on the back of the refrigerator.

Thus closing the doors and windows and opening the door of the refrigerator will not cool the room because the heat taken out from inside the refrigerator is still in the room. Also, all of the electric energy is not utilized, so this part will add to the temperature of the room
Q#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. 

Answer:  

A wooden chair will be selected because its thermal conductivity is much less than a metal chair. The wooden chair will allow very little heat of our body to pass through it  and very soon it's contact area will be equal to the body temperature, and we will not feel it cold.

Q#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 temperature equalize by radiation? Will the rate of heat gained by the colder sphere be proportional to T₂⁴-T₁⁴ as may be expected from Stefan's law? 

Answer:  

Both of the metal balls will radiate heat energy in all directions but with different rates. Consider the second ball which is on a higher temperature. It will radiate energy in all the directions but receive only a fraction of radiation by the first ball, so its temperature will fall. Similarly, the first ball will also radiate energy in all the direction and receive only a fraction of energy radiated by the first ball due to less area exposed to the radiation as in the first case. So the energy lost will be much more than the received. So its temperature will also fall. So the temperature will not equalize by radiation.

The rate of heat gained by the colder ball will not be proportional to T₂⁴ - T₁⁴ because the area through which heat is lost is different than the area on which heat is gained.     

Q#7

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

Answer:  

The circulation of air by the fan increases the evaporation of sweat on the body. It takes heat from the body which gives the cooling effect to the body and feels comfortable. 

Q#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. 

Answer:  

Thought the temperature at a high altitude is 500°C, due to very low pressure the air is thin and rarer. This rarer air is not capable to transfer heat of the surroundings to the body. On the other hand, due to the low pressure, the boiling point of water is very low. The water present in the skin and its outer surface will begin to boil without the help of outer heat received instead it will take the heat from the fluid itself and the temperature will fall and the animal will freeze to death. It should be noted that the boiling at low temperatures will not be felt like the boiling at the surface of earth. Also, the low pressure will have other implications like breathing difficulties and swelling of the body. 

Q#9

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

Answer:  

The temperature of the air is the same in both places. But in the sun the body receives the heat energy radiated by the sun and it feels pleasant on a cold winter day.

Q#10

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

Answer:  

The radiation from the earth during the night is partially blocked by the clouds and it feels warmer than the nights with the clean sky. 

Q#11

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

Answer:  

A white dress is a poor absorber of heat than a dark dress so the white dress is more comfortable.