Thermodynamics Explained: Heat, Temperature, Gas Laws and the Laws of Thermodynamics
Quick answer
Thermodynamics is the branch of physics that studies heat, temperature and how energy moves between systems. Its laws explain why heat flows from hot to cold, how engines turn heat into work, and why no machine can ever be 100% efficient.
Key takeaways
- Temperature measures how hot something is; heat is energy transferred because of a temperature difference.
- The energy needed to warm a substance is Q = mcΔT.
- Heat moves by conduction, convection and radiation.
- For an ideal gas, PV = nRT, with temperature always in kelvin.
- The first law (ΔU = Q − W) is energy conservation; the second law says entropy of an isolated system never decreases.
Why does a metal spoon get hot in a cup of tea? Why does a car engine need a radiator? Why does a bicycle pump warm up when you use it? Thermodynamics answers all of these questions with a few clear ideas about energy.
This guide starts with the basics of heat and temperature, then moves on to gas laws, the four laws of thermodynamics and heat engines. Each idea comes with a simple formula and a worked example, so you can see exactly how to use it.
What Is Thermodynamics?
Heat physics is the study of energy in the form of heat and work, and how it changes the state of matter. It began in the 1800s when engineers wanted to make steam engines more efficient. Today it is used in everything from refrigerators and power stations to weather forecasting and the chemistry of living cells.
In this field we talk about a system (the thing we are studying, such as a gas in a cylinder) and its surroundings (everything else). Energy can cross the boundary between them as heat or as work.
Temperature, Heat and Internal Energy
These three words are often mixed up in everyday speech, but in physics they mean different things.
| Term | Meaning | Unit |
|---|---|---|
| Temperature | How hot or cold an object is; related to the average kinetic energy of its particles | kelvin (K) or °C |
| Heat (Q) | Energy transferred from a hotter object to a colder one | joule (J) |
| Internal energy (U) | Total kinetic and potential energy of all particles in a system | joule (J) |
T(K) = T(°C) + 273.15
The kelvin scale starts at absolute zero (0 K = −273.15 °C), the lowest possible temperature. A change of 1 K is the same size as a change of 1 °C.
Common mistake: Never use degrees Celsius in gas law calculations. Always convert to kelvin first, or your answers will be wrong.
Specific Heat Capacity and Latent Heat
Specific heat capacity
Different materials need different amounts of energy to warm up. Water needs a lot, which is why the sea warms slowly in summer. The energy needed to raise the temperature of 1 kg of a substance by 1 K is its specific heat capacity, c.
Q = mcΔT
Q is energy in joules, m is mass in kg, c is specific heat capacity in J/(kg·K) and ΔT is the temperature change. For water, c ≈ 4,200 J/(kg·K).
Worked example: heating water
Question: How much energy is needed to heat 2 kg of water from 20 °C to 70 °C?
- ΔT = 70 − 20 = 50 K.
- Q = mcΔT = 2 × 4,200 × 50.
- Q = 420,000 J.
Answer: About 420 kJ of energy is needed.
Latent heat
When a substance melts or boils, it absorbs energy without its temperature changing. This hidden energy, called latent heat, breaks the bonds between particles.
Q = mL
L is the specific latent heat in J/kg. For ice melting, L ≈ 334,000 J/kg. For water boiling, L ≈ 2,260,000 J/kg.
Worked example: melting ice
Question: How much energy is needed to melt 0.5 kg of ice already at 0 °C?
- Use Q = mL.
- Q = 0.5 × 334,000.
- Q = 167,000 J.
Answer: About 167 kJ, with no change in temperature while it melts.
How Heat Is Transferred
Heat always flows naturally from a hotter place to a colder one. It travels in three ways.
- Conduction: energy passes from particle to particle through a material. Metals are good conductors; wood, air and plastic are good insulators.
- Convection: warm fluid (liquid or gas) becomes less dense and rises, while cooler fluid sinks, creating a current. This is how a radiator warms a room.
- Radiation: energy travels as infrared electromagnetic waves and needs no material at all. This is how the Sun warms Earth through empty space.
Tip: A vacuum flask reduces all three: a vacuum stops conduction and convection, and silvered walls reflect radiation.
The Gas Laws and PV = nRT
Gases are easy to compress and expand, so their pressure, volume and temperature are closely linked. Three simple laws describe what happens when one quantity is kept fixed.
| Law | What stays constant | Relationship |
|---|---|---|
| Boyle’s law | Temperature | P₁V₁ = P₂V₂ (pressure up, volume down) |
| Charles’s law | Pressure | V₁ ÷ T₁ = V₂ ÷ T₂ (heat a gas and it expands) |
| Gay-Lussac’s law | Volume | P₁ ÷ T₁ = P₂ ÷ T₂ (heat a sealed gas and its pressure rises) |
All three combine into the ideal gas law.
PV = nRT
P is pressure in pascals, V is volume in m³, n is the amount of gas in moles, R = 8.31 J/(mol·K) is the gas constant and T is temperature in kelvin.
Worked example: the ideal gas law
Question: What is the pressure of 1 mole of gas at 300 K in a 0.025 m³ container?
- Rearrange: P = nRT ÷ V.
- P = 1 × 8.31 × 300 ÷ 0.025.
- P = 99,720 Pa.
Answer: About 1.0 × 10⁵ Pa, which is close to normal atmospheric pressure.
The kinetic theory of gases explains these laws. Gas particles move randomly and hit the container walls. Heating them makes them move faster, so they hit harder and more often, which raises the pressure.
The Four Laws of Thermodynamics
Zeroth law: thermal equilibrium
If object A is at the same temperature as object C, and B is also at the same temperature as C, then A and B are at the same temperature. This simple idea is what makes thermometers work.
First law: energy is conserved
ΔU = Q − W
ΔU is the change in internal energy, Q is the heat added to the system and W is the work done by the system. Add heat and the gas can either warm up, do work by expanding, or both.
Second law: entropy and the direction of heat
Heat flows on its own only from hot to cold, never the other way. Another way to say this is that the total entropy (a measure of disorder, or how spread out energy is) of an isolated system never decreases. A fridge can move heat from cold to hot, but only because it uses electrical energy to do so.
Third law: absolute zero
As a system gets closer to absolute zero, its entropy approaches a minimum value. It is impossible to cool anything all the way to 0 K in a finite number of steps.
Heat Engines and Efficiency
A heat engine takes in heat from a hot source, turns part of it into useful work and releases the rest to a cold sink. Car engines, steam turbines and jet engines all work this way.
η = W ÷ QH and ηmax = 1 − TC ÷ TH
η is efficiency. The second formula gives the Carnot limit, the best any engine could do between temperatures TH and TC (both in kelvin).
Worked example: maximum efficiency
Question: An engine works between a hot source at 600 K and a cold sink at 300 K. What is its maximum possible efficiency?
- Use η = 1 − TC ÷ TH.
- η = 1 − 300 ÷ 600 = 1 − 0.5.
- η = 0.5.
Answer: 50%. A real engine would be less efficient because of friction and other losses.
The Carnot limit shows why power stations try to run at very high temperatures: a hotter source means a higher possible efficiency.
Common Mistakes With Heat and Gas Laws
- Using °C instead of K in gas law or efficiency calculations.
- Treating heat and temperature as the same thing.
- Forgetting that temperature stays constant during melting and boiling.
- Mixing up the sign of W in the first law. In this guide, W is work done by the system.
- Expecting an engine to reach 100% efficiency.
Go further: read this first law of thermodynamics guide with internal energy, heat and work examples and test yourself with ideal gas law MCQs with answers for physics exams.
Frequently Asked Questions
What is thermodynamics in simple terms?
Thermodynamics is the science of heat and energy. It explains how energy moves between objects, how heat can be turned into work and why some processes only happen in one direction.
What are the 4 laws of thermodynamics?
The zeroth law defines thermal equilibrium and temperature. The first law says energy is conserved (ΔU = Q − W). The second law says entropy of an isolated system never decreases, so heat flows naturally from hot to cold. The third law says absolute zero cannot be reached.
What is the difference between heat and temperature?
Temperature is a measure of how hot an object is and relates to the average energy of its particles. Heat is the energy that flows from a hotter object to a colder one because of their temperature difference.
Why can’t a heat engine be 100% efficient?
The second law requires some heat to be released to a colder sink. Only part of the input heat can become work, and the Carnot formula sets the upper limit.
What is the ideal gas law?
The ideal gas law is PV = nRT. It links the pressure, volume, amount and absolute temperature of a gas, and works well for most gases at normal temperatures and pressures.