Heat plays a pivotal role in thermodynamics, influencing the transfer and transformation of energy within and between systems. Its understanding is essential not just in physics and chemistry, but also in practical applications. The principles of heat transfer are fundamental in designing countless devices and systems, from household appliances to industrial machinery.

### Heat Definition

**Heat** is the thermal energy transfer between systems or bodies due to a temperature difference. Thermal energy, in turn, is the kinetic energy of vibrating and colliding particles. Heat occurs spontaneously from a hotter body to a colder one. It is important to note that heat is energy in transit; it is not stored as an internal property of an object.

### Symbol and Units

The usual symbol for heat is ‘Q’. The standard unit of heat in the International System of Units (SI) is the joule (J). Another unit is the calorie (cal), with 1 calorie being the amount of heat required to raise the temperature of 1 gram of water by 1 degree Celsius at atmospheric pressure. The British thermal unit (BTU) is another common unit.

### Sign Convention

In physics equations, the sign convention for heat transfer indicates the direction of energy flow. Heat absorbed by a system is positive (Q > 0), indicating that the system’s internal energy increases. Conversely, heat released by a system is negative (Q < 0), signifying a decrease in internal energy.

### Difference Between Heat and Temperature

Heat and temperature are closely related but distinct concepts. Temperature is a measure of the average kinetic energy of the particles in a substance, and it dictates the direction of heat transfer. Heat, on the other hand, is the transfer of energy due to a temperature difference. It is the process of energy movement, while temperature is a state function that describes a system’s thermal state.

### How Matter Gains and Loses Heat

Matter gains or loses heat through the processes of conduction, convection, and radiation:

**Conduction**is the transfer of heat through a material without the material itself moving. It occurs best in solids.**Convection**involves the movement of a fluid (liquid or gas), carrying heat with it. For example, in boiling water, hot water rises and cooler water descends.**Radiation**is the transfer of heat through electromagnetic waves and can occur in a vacuum (like heat from the sun reaching Earth).

### Heat Formula Using Heat Capacity

One method of calculating the amount of heat transfer to or from a substance is using its heat capacity. Heat capacity is the amount of heat required to change the temperature of a certain quantity of the substance by one degree. The equation is:

*Q*=*mc*Δ*T*

Where:

*Q*is the heat added or removed,*m*is the mass of the substance,*c*is the specific heat capacity (energy required to raise the temperature of 1 kg of the substance by 1 degree Celsius),- Δ
*T*is the change in temperature.

**Example Calculation**

For instance, calculate the heat required to raise the temperature of 2 kg of water from 20°C to 100°C:

Given:

- m = 2 kg (mass of water),
- c = 4.186 kJ/kg°C (specific heat capacity of water),
- Δ
*T*= 100°*C*− 20°*C*=80°*C*

The heat Q required is: Q = 2 kg × 4.186 kJ/kg°C × 80°C = 669.76 kJ

### Thermal Equilibrium and the Zeroth Law of Thermodynamics

Thermal equilibrium is a concept where two objects in contact do not exchange heat, as they are at the same temperature. The Zeroth Law of Thermodynamics states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other. This law forms the basis of temperature measurement and underscores the fundamental nature of temperature as a property of matter.

### Heat and Entropy

The relationship between heat transfer, entropy, and the Second Law of Thermodynamics illustrates a fundamental principle of the natural world: energy tends to disperse and systems move towards a state of higher entropy.

Entropy, denoted as *S*, is a measure of disorder or randomness in a system. In thermodynamic terms, it quantifies the number of ways a system can be arranged, often interpreted as a measure of uncertainty or the dispersal of energy within a system.

The mathematical expression for entropy change, Δ*S*, when a quantity of heat *Q* is added or removed from a system at a temperature *T*, is:

Δ*S*=*TQ*

Q = Δ*S*/*T*

This formula applies when the heat transfer occurs at a constant temperature.

### Second Law of Thermodynamics

The Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. In other words, the universe tends toward greater disorder or entropy.

**Example Problem**

For example, consider 100 J of heat being transferred from a hot reservoir at 400 K to a cold reservoir at 300 K. Calculate the entropy change of the system.

**Solution:**

**Entropy Change in the Hot Reservoir (Entropy Decrease):**

Using Δ*S*=*TQ*, the entropy change of the hot reservoir (denoted as Δ*S*_{hot}) is:

Δ*S*_{hot}= −100 J / 400 K = −0.25 J/K

The negative sign indicates a decrease in entropy.**Entropy Change in the Cold Reservoir (Entropy Increase):**

Similarly, the entropy change of the cold reservoir (denoted as Δ*S*_{cold}) is:

Δ*S*_{cold}= 100 J / 400 K ≈ 0.33 J/K**Total Entropy Change of the System:**

Δ*S*_{system}= Δ*S*_{hot}+ Δ*S*_{cold} = −0.25 J/K + 0.33 J/K = 0.08 J/K

The positive total entropy change (Δ*S*_{system} > 0) is consistent with the Second Law of Thermodynamics, as the entropy increases with this heat transfer.

### Heat Transfer and Entropy

When heat transfers from one body to another, the entropy of the system changes. Heat flows naturally from a higher temperature body to a lower temperature body. In this process:

- The entropy of the body losing heat decreases.
- The entropy of the body gaining heat increases.
- The net change in the universe’s entropy is positive.

### Heat and Enthalpy

Enthalpy, denoted as *H*, is a measure of the total heat content of a thermodynamic system. It’s useful for calculating the heat change in processes occurring at constant pressure. Enthalpy is defined as:

*H* = *U* + *PV*

Where:

*U*is the internal energy of the system,*P*is the pressure,*V*is the volume.

For processes at constant pressure, the change in enthalpy Δ*H* equals the heat absorbed or released:

Δ*H* = Q_{p}

Where Q_{p} is the heat transfer at constant pressure.

**Example Problem**

For example, suppose 100 grams of water is heated from 20°C to 100°C at constant pressure. Calculate the heat absorbed by the water and the change in enthalpy. Assume the specific heat capacity of water is 4.18 J/g°C.

**Solution:**

**Calculate the Heat Absorbed (***Q*):

Given:*m*=100g

*c*=4.18J/g°C

- Δ
*T*=100°*C*−20°*C*=80°*C*

*Q*=*mc*Δ*T*:*Q*= 100 × 4.18 × 80 = 33440 J**Calculate the Change in Enthalpy (Δ***H*):

For a process at constant pressure, Δ*H*=*Q*.

Δ*H*=33440J

The heat absorbed by the water is 33,440 Joules, and the change in enthalpy of the water is also 33,440 Joules under these conditions.

This example illustrates the direct relationship between heat and enthalpy in constant pressure scenarios, common in chemistry and other areas of thermodynamics. Enthalpy is particularly useful in describing heat changes in chemical reactions and reaction and formation enthalpies.

### References

- Atkins, P., de Paula, J. (2010).
*Physical Chemistry*(9th ed.). Oxford University Press. ISBN 978-0-19-954337-3. - Joule, J.P. (1845).”On the Mechanical Equivalent of Heat”.
*Philosophical Transactions of the Royal Society of London*. 140: 61–82. 1850. doi:10.1098/rstl.1850.0004 - Kondepudi, D. (2008).
*Introduction to Modern Thermodynamics*. Chichester UK: Wiley. ISBN 978-0-470-01598-8. - Van Wylen, Gordon; Sonntag, Richard (1978).
*Fundamentals of Classical Thermodynamics*(2nd ed.). Chapter 4.7, Definition of Heat: John Wiley & Sons. ISBN 0-471-04188-2.