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Heat formulas and equations are used to calculate the heat of substances by measuring the expansion rate of various objects. A body tends to expand when subjected to excessive heat. Expansion takes place in all gases, solids, and liquids.
- In the heat formula, the direction of flow of heat is from a substance at a higher temperature to a substance at a lower temperature.
- The SI unit of heat is the same as that of energy, that is, calories or joules.
Key Terms: Heat Formula, Heat, Specific Heat Formula, Specific Heat Capacity Formula, Latent Heat Formula, Heat Transfer, Energy, Temperature
Key Highlights
- Heat is a form of thermal energy that is transferred between two systems due to difference in temperature.
- It flows from a higher temperature object to a lower temperature object via conduction, convection, or radiation.
- Heat is produced by the effect of temperature whose value cannot be interchanged.
- The greater the value of thermal conductivity for a material, the more swiftly it will conduct and transfer heat.
- The amount of heat required to bring a certain level of growth in bodies is calculated with the help of instruments.
What is the Concept behind Heat?
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Thermal physics is a branch of physics that deals with the temperatures and heat of an object or body. It uses various heat formulas and equations to describe the heat of a substance.
- Heat is a type of energy that produces a change in the temperature of any substance to maintain heat equilibrium in nature.
- It means whenever the temperature of a body increases, it produces heat.
- This transfer of energy strictly follows the law of conservation of energy.
- The dimensional formula of heat is given as [M1 L2 T-2], which is derived using the analogy of heat to energy.
- We use heat energy for daily activities like ironing, cooking, transportation and recreation.
Heat Formula
Specific Heat Formula
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In thermodynamics, the ratio of the amount of heat required to raise the temperature of an object by a degree to the amount of heat needed to raise the temperature of an equivalent liquid by the same degree is called specific heat.
- The formula depends on the value of the pressure, volume and temperature.
- The SI unit of the specific heat formula is Joule/Kg Kelvin (J/Kg K).
- We use the concept to understand how much heat is required to raise the temperature of an object by one degree Celsius.
- Specific heat formula refers to the ratio between the specific heat capacities of a substance at a given temperature.
- Mathematically, it can be represented as:
C = ΔQ/ mΔt
Where,
- Δ Q: heat gained or lost
- Δ T : difference in temperature
- m: mass
- Δ T = (Tf – Ti), where final temperature is Tf and initial temperature is Ti .
Specific Heat Capacity Formula
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Specific heat capacity is a relative term used instead of using specific heat. It denotes the energy needed to change the temperature of a unit mass of the substance to one degree.
- Specific heat capacity is not a constant unit in thermodynamics and varies from place to place.
- It is measured in Joules per kilogram per Kelvin (J kg-1 K-1).
- Specific heat capacity depends on physical properties, like temperature, volume, and pressure of the surrounding area and the object.
- This heat capacity is a type of thermal inertia indicating the resistance of a material to change in its temperature.
- The specific heat capacity formula is given as:
Q = C m △t
where,
- Q: heat absorbed by a body
- m: mass of the body
- △t: change in temperature
- C = Specific heat capacity of a substance
Derivation of Specific Heat Capacity Formula
We know, the energy needed to increase the temperature of the object is directly proportional to its temperature and mass. It is given by,
Q ∝ ΔT
where ΔT is the change in temperature of an object.
Q ∝ m
From the above two proportionalities, we get,
Q ∝ m ΔT
Q = C m ΔT
where C is proportionality constant, known as specific heat
Thus, specific heat formula, C is given by,
C = Q / m ΔT joules kg-1 oC-1
The below table lists specific heat capacities of different compounds at room temperature and atmospheric pressure.
| Substance | Specific heat capacity (J kg-1 K-1) |
|---|---|
| Ice | 2060 |
| Iron | 450 |
| Edible oil | 1965 |
| Mercury | 140 |
| Glass | 840 |
| Kerosene | 2118 |
| Water | 4186 |
| Aluminium | 900 |
| Carbon | 506.5 |
| Tungsten | 134.4 |
| Lead | 127.7 |
| Copper | 386.4 |
| Silver | 236.1 |
Latent Heat Formula
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Latent heat is the amount of heat that is radiated or absorbed at constant temperature and pressure. It depends upon the value of the heat property called enthalpy.
- It is also defined as the heat needed by a body to maintain a constant temperature.
- Latent Heat is divided into three categories, namely Latent Heat of Fusion, Latent Heat of Vaporization and Latent Heat of Sublimation.
- The two examples of this type of heat are Latent heat of vaporization and Latent heat of Freezing.
- The SI unit of the latent heat formula is Cal/g, joules per gram (J/g), or kilojoules per kilogram (kJ/kg).
- It can change its state either from gas to liquid or liquid to solid and vice versa.
- Mathematically, it can be represented as:
Q = m x L
where
- Q: amount of heat that is absorbed or released
- m: mass of the substance and
- L: Specific Latent Heat
The below table gives a list of various substances with their latent heat.
| Substance | Melting point (C) | Latent heat (105 J kg-1) | Boiling point (C) | Latent heat (105 J kg-1) |
|---|---|---|---|---|
| Water | 0 | 3.33 | 100 | 22.6 |
| Gold | 1063 | 0.645 | 2660 | 15.8 |
| Lead | 328 | 0.25 | 1744 | 8.67 |
| Oxygen | -219 | 0.14 | -183 | 2.1 |
| Nitrogen | -210 | 0.26 | -196 | 2.0 |
| Ethyl alcohol | -114 | 1.0 | 78 | 8.5 |
| Mercury | -39 | 0.12 | 357 | 2.7 |
Sample questions
Ques. Answer: (A) Do ideal gases obey the heat formula?
(B) What is the formula for heat? (2 marks)
Ans. (A) Gases obey gas laws, i.e. PV = RT. Gases are poor conductors of heat. Even in ideal conditions, they do not obey the heat formula.
(B) The formula for heat, Q = C m ΔT. It is measured in Joules or calories.
Ques. How would you get the final temperature in a heat formula if not given the mass? (2 marks)
Ans. If the mass is not given in the data, we can use molar mass or weight for our calculations. If that is also not given, we can use variables and derive a general equation for such conditions.
Ques. What is Thermal Capacity? (2 marks)
Ans. The thermal capacity of a body is the quantity of heat required to raise the temperature of the whole body through a unit degree. It is measured in calories per °C or joule per K. If Q be the amount of heat needed to produce a change in temperature (Δt) of the substance, then the thermal capacity of the substance is given by
S = \(\frac {Q} {\Delta t}\)
The dimensional formula of heat capacity is [ML2T-2K-1]
Ques. What are three ways heat is transferred? (2 marks)
Ans. Heat is transferred from higher temperature to lower temperature in three ways – conduction (physical contact of bodies), convection (heat transfer without touch, but the body gets heated due to vibration of individual particles within a body), and radiation (transfer of energy by heatwaves from one medium to another).
Ques. What is specific heat capacity? (3 marks)
Ans. The specific heat capacity (also referred to as specific heat) of a substance is the amount of heat required to raise the temperature of a unit mass of substance through 1 °C. It is measured in cal g-1(°C)-1 or J kg-1 K-1. The specific heat capacity of a substance is given by
S = \(\frac {1}{M}\) \(\frac {Q} {\Delta t}\)
where m is mass of substance and Q is the heat required to change its temperature Δt.
- Molar specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of 1 mole of the substance by 1°C.
It is given by
- The unit of molar specific heat capacity is J mole-1 K-1 in SI system and Cal mol-1 °C-1 in CGS system.
- The dimensional formula of molar specific heat capacity is [ML2T-2 K-2 mole-1].
Ques. What is the dimensional formula of specific heat capacity? (1 mark)
Ans. Specific heat capacity is given by C = Q / m ΔT joules kg-1 oC-1. Converting them to mass, length and time, we get the dimensional formula as L2 T-2 K-1.
Ques. What is Latent Heat? (3 marks)
Ans. Latent heat of a substance is the amount of heat energy required to change the state of a unit mass of the substance from solid to liquid or from liquid to gas/vapour without any change in temperature.
- The latent heat of fusion (Lf) is the heat per unit mass required to change a substance from solid into liquid at the same temperature and pressure.
- The latent heat of vaporisation (Lv) is the heat per unit mass required to change a substance from liquid to vapour state without a change in temperature and pressure.
Ques. What is an example of kinetic energy into heat energy? (2 marks)
Ans. Kinetic energy occurs due to the motion of particles within a substance. Almost every kinetic energy is converted into heat energy. Some common examples are lighting a matchstick, heating of braking system by the continuous movement of a car, heating of wires due to the flow of electricity, etc.
Ques. What is transfer of heat? (3 marks)
Ans. Heat can be transferred from one place to another by three different methods, namely, conduction, convection and radiation. Conduction usually takes place in solids, convection in liquids and gases, and no medium is required for radiation.
(i) Conduction: According to Maxwell, conduction is the flow of heat through an unequally heated body from places of higher temperature to those of lower temperature. Rate of heat transfer is given by
H = \(\frac {Q} {T}\) = \(\frac {KA (T_1 - T_2)}{l}\)
where K is called Thermal Conductivity and A is the area of cross-section.
(ii) Convection: Maxwell defines convection as the flow of heat by the motion of the hot body itself carrying its heat with it.
(iii) Radiation: Radiation is the mode of heat transfer in which heat travels directly from one place to another without the agency of any intervening medium.
- Thermal conductivity is defined as heat energy transferred in unit time from unit area having a unit difference in temperature over unit length. It is expressed in Js-1 m-1 °C-1 or W-1 K-1
Ques. A 100 gram lead cube is heated from 30 to 70 degrees Celsius. How much power did it take to heat this lead? Lead has a specific heat of 0.129 J/g°C? (3 marks)
Ans. Let’s start with the factors we already know.
c = 0.129 J/g°C m = 500 g
∆T = (Tfinal – Tinitial)
(70 °C – 30 °C) = 40 °C
Fill in the blanks in the above-mentioned specific heat equation.
mc∆T = Q
Q = (100 grams) (0.129 J/g°C) (40 degrees Celsius)
516 J = Q
The lead cube was heated from 30°C to 70°C with 516 Joules of energy.
Ques. What is the latent heat of a substance with a mass of 20 kg if the amount of heat needed by it for the transition phase is 200 Kcal? (2 marks)
Ans. Here,
Q = 200 Kcal
M = 20 kg
The latent heat formula is,
L = Q/m
Applying the values, we get,
L = 200/20
= 10 k.cal kg-1
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