Heat is a form of energy that is transferred between a system and its surrounding as a result of temperature differences. The expansion due to an increase in temperature is known as thermal expansion. There are three types of thermal expansion, namely linear, superficial and volume expansion.
Types of Thermal Expansion
1. Linear Expansion
When there is any change in the length of a body due to heating, then the expansion is called longitudinal or linear expansion.
Coefficient of Expansion: Δ1 = Change in length and Δt = Change in Temperature
2. Superficial Expansion
When there is any change in the area of a body due to heating, then the expansion is called axial or superficial expansion.
Coefficient of Expansion: ΔA = Change in Area and Δt = Change in Temperature
3. Volumetric Expansion
When there is any change in the volume of a body due to heating, then the expansion is called volumetric or cubic expansion.
Coefficient of Expansion: ΔV = Change in volume and Δt = Change in Temperature
If α1, α2, and α3 are the coefficient of linear expansion in X, Y and Z directions, then,
Case 1: For Isotropic Solids
α = α1 = α2 = α3, β = 2α γ = 3α
Case 2: For Anisotropic Solids
β = α1 + α2 and γ = α1 + α2+ α3
Thermal Stress
If the temperature of a rod of length l0 clamped between two fixed walls separated by the same distance l0 is changed by amount Δt, then
Case 1: α is constant
Stress = F / A and Strain = Δl / lo
Therefore,
Case 2: α is not constant
A. If α varies with distance [α = ax + b]
Total thermal expansion
B. If α varies with temperature [α = f (T)]
Variation in Density: Density decreases with an increase in temperature because of the increase in volume and vice-versa, i.e.,
γ is the coefficient of volumetric expansion.
d0 is the initial density.
Δt is the change in temperature.
Special Case: The density of water is maximum at 4°C. Its density increases from 0 °C to 4°C. From 4°C to higher temperatures, d is positive.
Modes of Heat Transfer
While conduction is the transfer of heat energy by direct contact, convection is the movement of heat by the actual motion of matter; radiation is the transfer of energy with the help of electromagnetic waves.
| Heat Transfer | Conduction | Convection | Radiation |
| Definition | Heat is transferred between objects by direct contact. | Energy transition (heat transfer) occurs within the fluid. | Heat transmission is done without any physical contact between objects. |
| Representation | How heat travels between objects in direct contact. | How heat passes through fluids. | How heat flows through empty spaces. |
| Occurrence | Occurs in solids through molecular collisions. | Occurs in fluids by the actual flow of matter. | Occurs at a distance and does not heat the intervening substance. |
| Causes | Temperature difference | Density difference | Occurs from all objects at a temperature greater than 0 Kelvin. |
| Speed | Slow | Slow | Fast |
| Law of reflection and refraction | Does not follow | Does not follow | Follows |
| Transfer of heat | Uses a heated solid substance | Uses an intermediate substance | Uses electromagnetic waves |
Stefan-Boltzmann Law:
It states that the net radiant heat energy emitted from an object is proportional to the 4th power of its absolute temperature.
Radiation Power:
If Ts is the Surrounding Temperature: [Black Body]
Emissive Power or Emissivity e = Heat from given body / Heat from a black body
Newton’s Law of Cooling:
It states that the rate of change of the temperature (T) of an object is proportional to the difference between its own temperature and the temperature of its surroundings.
T(t) = Ts + (To – Ts ) e – k t
Where,
Ts = Surrounding Temperature
To = Initial temperature of the body
T (t) = Temperature of the body at time t
k = Cooling constant
Wien’s Black Body Radiation:
At any temperature T greater than 0 Kelvin, the body emits energy radiations of all wavelengths. According to Wien’s displacement law, if the wavelength (λ) corresponding to the maximum energy is λmax, then,
λmax T = b
Where,
T = Temperature of the body
b = Wien’s Constant
Calorimetry
It is the measurement of changes in the state variables of an object for the purpose of deriving the transfer of heat associated with changes in its state, either due to phase transitions, physical changes or chemical reactions, under specified constraints. A calorimeter is a device using which calorimetry is performed.
The amount of heat required to raise the temperature of 1 gram of water from 14.5° C to 15.5°C at standard temperature and pressure (STP) is 1 calorie.
Heat transfer in phase change:
Q = mL
Where,
L = Latent heat of substance in Cal gm-1 0C-1 or in Kcal kg-1 0C-1
Lsteam = 540 cal/ gm
Lice = 80 cal/ gm for ice
Frequently Asked Questions on Heat Transfer and Calorimetry
Define calorimetry.
Calorimetry is the branch of science that deals with the measurement of heat energy.
What are the modes of heat transfer?
Conduction
Convection
Radiation
Ice is covered in gunny bags to prevent the melting of ice. Explain why.
The material of the gunny bag is a bad conductor of heat. Moreover, the air filled in the pores of the gunny bags is also a bad conductor of heat. So the flow of heat from outside to the ice inside the gunny bag will not be allowed. Hence, ice is prevented by melting when it is kept inside the gunny bag.
Why do we feel warm in woollen clothes?
Wool itself is a bad conductor of heat. Also, the pores in the woollen clothes enclose air in them. This air will reduce the thermal conductivity of the clothes. So woollen clothes will allow only less amount of heat to flow out, and hence, we feel warmer.
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