Heat and Work in Thermodynamics

In thermodynamics, heat and work are fundamental forms of energy transfer between a system and its surroundings. Understanding them is crucial because they govern energy conversion, processes, and the laws of thermodynamics. Heat and work are not properties of a system themselves but describe energy in transit.

This post provides a complete overview of heat and work, including their definitions, units, types, mathematical treatment, examples, and significance in real-life systems.

1. Introduction

Energy transfer is central to thermodynamics. When a system undergoes a change in state—such as a change in temperature, pressure, or volume—energy is exchanged with its surroundings. This energy exchange occurs in two primary ways:

Heat (Q): Energy transfer due to a temperature difference.
Work (W): Energy transfer due to a force acting over a distance.

While both heat and work result in changes in a system’s internal energy, they differ in mechanism, measurement, and conceptual understanding.

2. Heat (Q)

2.1 Definition

Heat is defined as:

The energy transferred between a system and its surroundings due to a temperature difference.

Key points:

Heat flows from higher temperature to lower temperature spontaneously.
It is energy in transit, not stored within the system.
Symbol: QQQ
SI unit: Joule (J)
1 calorie (cal) = 4.186 J

2.2 Modes of Heat Transfer

Heat can be transferred in three main ways:

Conduction: Transfer of heat through a medium without macroscopic motion of the substance.
- Occurs mainly in solids.
- Example: Heating one end of a metal rod transfers energy to the other end.
- Fourier’s Law:
Q=−kAdTdxtQ = -k A \frac{dT}{dx} tQ=−kAdxdTt Where kkk = thermal conductivity, AAA = area, dT/dxdT/dxdT/dx = temperature gradient, ttt = time.
Convection: Transfer of heat through a fluid due to bulk motion.
- Occurs in liquids and gases.
- Example: Boiling water circulates heat through convection currents.
- Newton’s Law of Cooling:
Q=hAΔTtQ = h A \Delta T tQ=hAΔTt Where hhh = convective heat transfer coefficient.
Radiation: Transfer of heat through electromagnetic waves.
- Does not require a medium.
- Example: Heat from the Sun reaches Earth.
- Stefan-Boltzmann Law:
Q=σAeT4tQ = \sigma A e T^4 tQ=σAeT4t Where σ\sigmaσ = Stefan-Boltzmann constant, eee = emissivity, TTT = temperature.

2.3 Heat Capacity and Specific Heat

Heat capacity (C) is the amount of heat required to raise the temperature of a body by 1°C or 1 K: C=QΔTC = \frac{Q}{\Delta T}C=ΔTQ

Specific heat (c) is the heat required to raise the temperature of 1 kg of a substance by 1°C or 1 K: Q=mcΔTQ = mc\Delta TQ=mcΔT

Where mmm = mass of the substance, ΔT\Delta TΔT = temperature change.

Examples:

Water: c=4186 J/kg\cdotpKc = 4186 \text{ J/kg·K}c=4186 J/kg\cdotpK
Aluminum: c=900 J/kg\cdotpKc = 900 \text{ J/kg·K}c=900 J/kg\cdotpK

2.4 Latent Heat

When a substance changes phase (solid ↔ liquid ↔ gas) without a change in temperature, heat is called latent heat.

Latent heat of fusion (LfL_fLf): Heat required to convert solid to liquid.
Latent heat of vaporization (LvL_vLv): Heat required to convert liquid to gas.

Formula: Q=mLQ = mLQ=mL

Where LLL = latent heat, mmm = mass of substance.

3. Work (W)

3.1 Definition

Work in thermodynamics is defined as:

The energy transferred when a force acts through a distance or when a system expands or contracts against external pressure.

Key points:

Symbol: WWW
SI unit: Joule (J)
Work is positive when done by the system on the surroundings and negative when done on the system by the surroundings.

3.2 Types of Thermodynamic Work

Mechanical Work: Work done due to volume change against external pressure:

W=∫P dVW = \int P \, dVW=∫PdV

PPP = pressure, dVdVdV = change in volume.
Example: Gas expansion in a piston.

Shaft Work: Work done by rotating machinery, turbines, or fans.

W=τθW = \tau \thetaW=τθ

Where τ\tauτ = torque, θ\thetaθ = angular displacement.

Electrical Work: Work done in moving electric charges:

W=∫V dQW = \int V \, dQW=∫VdQ

Where VVV = voltage, dQdQdQ = charge transfer.

Boundary Work: Work done by or on the system when its boundary moves:

δW=P dV\delta W = P \, dVδW=PdV

Common in pistons, compressors, and cylinders.

3.3 Work in Various Thermodynamic Processes

Isobaric Process (constant pressure):

W=PΔVW = P \Delta VW=PΔV

Isochoric Process (constant volume):

W=0W = 0W=0

Isothermal Process (constant temperature) for ideal gas:

W=nRTln⁡VfViW = nRT \ln \frac{V_f}{V_i}W=nRTlnViVf

Adiabatic Process (no heat exchange) for ideal gas:

W=PiVi−PfVfγ−1W = \frac{P_i V_i – P_f V_f}{\gamma – 1}W=γ−1PiVi−PfVf

Where γ=CpCv\gamma = \frac{C_p}{C_v}γ=CvCp = heat capacity ratio.

4. Relationship Between Heat, Work, and Internal Energy

The first law of thermodynamics links heat, work, and internal energy: ΔU=Q−W\Delta U = Q – WΔU=Q−W

Where:

ΔU\Delta UΔU = change in internal energy (extensive property)
QQQ = heat added to the system (positive if absorbed)
WWW = work done by the system (positive if work is done on surroundings)

Key Points:

Heat increases internal energy or does work.
Work done on the system increases internal energy.
Work done by the system decreases internal energy.

Example:

Compressing gas in a piston (work done on the gas) increases internal energy.
Gas expansion against pressure (work done by the gas) decreases internal energy unless heat is supplied.

5. Sign Conventions in Thermodynamics

Sign conventions are important for correct calculations:

Process	Heat (Q)	Work (W)
Energy added to system	Positive	Negative (work done on surroundings)
Energy removed from system	Negative	Positive (work done on system)

Different textbooks may adopt slightly different conventions, but consistency is essential.

6. Heat and Work as Path Functions

Heat (Q) and work (W) are path-dependent functions.
Their values depend on the process, not just the initial and final states.
Internal energy (U) is a state function; its change depends only on initial and final states:

ΔU=Uf−Ui\Delta U = U_f – U_iΔU=Uf−Ui

Example: Two paths from state A to state B:

Path 1: Q1, W1
Path 2: Q2, W2

Even if ΔU\Delta UΔU is the same, QQQ and WWW may differ: ΔU=Q1−W1=Q2−W2\Delta U = Q_1 – W_1 = Q_2 – W_2ΔU=Q1−W1=Q2−W2

7. Heat and Work in Cyclic Processes

A cyclic process returns a system to its initial state (ΔU=0\Delta U = 0ΔU=0): Q=WQ = WQ=W

Total heat added equals total work done.
Basis for heat engines and refrigerators.

Examples:

Carnot Engine: Heat absorbed from hot reservoir → Work done → Heat rejected to cold reservoir.
Steam Turbine: Heat from steam → Work on turbine → Remaining heat released.

8. Graphical Representation

8.1 PV Diagram

Area under a PV curve represents work done.
Expansion → positive work; compression → negative work.

8.2 TS Diagram

Area under TS curve represents heat transfer.
Useful in analyzing efficiency of heat engines.

9. Practical Examples

Boiling Water in a Pot:
- Heat flows from stove to water → increases internal energy → water boils.
- Work done is negligible unless water expands against atmospheric pressure.
Piston-Cylinder Engine:
- Fuel combustion adds heat → increases gas internal energy → gas expands → does work on piston.
Refrigerator:
- Work is done on the refrigerant → heat absorbed from cold chamber → rejected to surroundings.
Steam Turbine:
- Heat from steam → gas expands → does work on blades → generates electricity.

10. Heat Engines and Thermodynamic Cycles

Heat engine: Converts heat into work.
Efficiency (η\etaη) depends on heat and work:

η=WQH=QH−QCQH=1−QCQH\eta = \frac{W}{Q_H} = \frac{Q_H – Q_C}{Q_H} = 1 – \frac{Q_C}{Q_H}η=QHW=QHQH−QC=1−QHQC

QHQ_HQH = heat from hot reservoir, QCQ_CQC = heat rejected to cold reservoir.

Example: Carnot cycle efficiency depends on reservoir temperatures: η=1−TCTH\eta = 1 – \frac{T_C}{T_H}η=1−THTC

11. Measurement of Heat and Work

Heat: Measured using calorimeters.
Work: Measured using mechanical devices, force-displacement sensors, or pressure-volume work calculations.
Instruments are designed according to the process type.

12. Key Differences Between Heat and Work

Feature	Heat (Q)	Work (W)
Definition	Energy transfer due to temperature difference	Energy transfer due to force or motion
Path dependence	Yes	Yes
Units	Joules (J)	Joules (J)
Direction	Always high → low temperature	Depends on system or surroundings
Mechanism	Thermal interaction	Mechanical, electrical, or boundary movement

13. Summary

Heat and work are mechanisms of energy transfer:

Heat flows due to temperature differences.
Work is done by force acting over a distance or volume change.
Both are path functions; internal energy is a state function.
Understanding heat and work is essential for:
- Engines: Steam engines, internal combustion engines.
- Refrigerators and air conditioners.
- Power plants: Steam, nuclear, and gas turbines.
- Chemical reactions: Exothermic and endothermic processes.

Correct application of heat and work concepts is the foundation of thermodynamics, energy engineering, and physical sciences.

14. Key Formulas Recap

Heat added: Q=mcΔTQ = mc\Delta TQ=mcΔT
Latent heat: Q=mLQ = mLQ=mL
Work in expansion/compression: W=∫P dVW = \int P \, dVW=∫PdV
First law of thermodynamics: ΔU=Q−W\Delta U = Q – WΔU=Q−W
Work in isothermal process: W=nRTln⁡VfViW = nRT \ln\frac{V_f}{V_i}W=nRTlnViVf
Efficiency of heat engine: η=WQH=1−QCQH\eta = \frac{W}{Q_H} = 1 – \frac{Q_C}{Q_H}η=QHW=1−QHQC