Heat and Temperature: A Complete Guide to Understanding How Energy Moves Between Bodies
From the warmth of rubbing your hands together to the absolute zero of the Kelvin scale — everything you need to know, explained clearly.
1. What Is Heat
Heat
? Understanding Internal Energy
Have you ever wondered why your hands feel warm after rubbing them together? Or why two vehicles involved in a crash become extremely hot — sometimes even catching fire? These everyday experiences are your first encounter with one of the most fundamental ideas in physics: the relationship between heat and internal energy.
When you rub your hands together, you are doing mechanical work. That work does not simply disappear. Instead, it converts into what physicists call internal energy — the energy stored within the molecules of the material itself. The molecules start vibrating faster, and you feel that as warmth. The same thing happens when a bicycle tyre rubs against the road, when a block slides across a rough surface, or when an aeroplane crashes. In every case, mechanical energy is lost and the bodies involved become hot.
This leads to a powerful conclusion: a hot body has more internal energy than an otherwise identical cold body. The hotter the body, the faster its molecules are moving on average, and the greater its internal energy.
Now consider what happens when you place a hot cup of tea next to a cold glass of water. The tea cools down. The water warms up. Energy has moved from the hot body to the cold body. This transfer of energy happened without any mechanical work being done — no force moved through a distance, no piston was pushed. This non-mechanical transfer of energy from one body to another is what we call heat.
Heat is the energy transferred from one body to another solely due to a difference in temperature, without any mechanical work being involved in the transfer process.
It is important to distinguish heat from internal energy. Internal energy is what a body has. Heat is what gets transferred between bodies. You cannot say a body “contains” a certain amount of heat — you can only say that a certain amount of heat flowed into or out of it.
2. The Zeroth Law of Thermodynamics
Once we understand that heat flows between bodies at different temperatures, a natural question arises: how do we know when two bodies are at the same temperature? The answer lies in the concept of thermal equilibrium.
Two bodies are said to be in thermal equilibrium if, when placed in contact, no heat flows between them. That means their temperatures are equal. Simple enough.
But now consider three bodies: A, B, and C. Suppose A and B are in thermal equilibrium (no heat flows between them). And suppose A and C are also in thermal equilibrium. What can we say about B and C? Will heat flow between them if they are placed in contact?
From observation and experience, the answer is: no. B and C will also be found to be in thermal equilibrium. This fact — obvious as it may seem — is known as the Zeroth Law of Thermodynamics:
If two bodies A and B are in thermal equilibrium, and A and C are also in thermal equilibrium, then B and C are in thermal equilibrium with each other.
Why is this called the “Zeroth” law? Because it was recognised after the First and Second Laws of Thermodynamics were already established, but it is logically more fundamental — it has to come before them. So it was numbered zero.
The Zeroth Law is what makes the concept of temperature meaningful. Because of this law, we can say that all bodies in thermal equilibrium share a common property — and we give that property a number. We call it temperature. Bodies with higher temperature are hotter; bodies with lower temperature are colder. Heat always flows from the body at higher temperature to the body at lower temperature when they are placed in contact.
3. Defining a Scale of Temperature
Saying one body is “hotter” than another is useful, but science demands numbers. To assign a numerical value to temperature, we need a thermometric property — a property of some substance that changes measurably and monotonically (always increasing or always decreasing) with temperature.
For a useful temperature scale, we typically:
Step 1: Choose a substance and identify a measurable property. For mercury in a glass tube, the relevant property is the length of the mercury column. For a metal wire, it is electrical resistance.
Step 2: Choose two fixed reference points that can be reliably reproduced in a laboratory. The most common choices are the ice point (melting ice at 1 atm, assigned 0°C) and the steam point (boiling water at 1 atm, assigned 100°C).
Step 3: Assume a linear relationship between the thermometric property and temperature. This gives a formula you can use to find any temperature from a measured value of the property.
Different substances give different scales, and these scales only agree at the two fixed points. This is an important limitation we will address when we reach the ideal gas temperature scale.
4. Mercury Thermometer and the Centigrade Scale
The mercury-in-glass thermometer is one of the oldest and most familiar thermometers. A small bulb containing mercury is connected to a narrow glass capillary. As temperature rises, mercury expands and its column length in the capillary increases.
Let’s say the mercury column length is l₀ at the ice point (0°C) and l₁₀₀ at the steam point (100°C). For any other mercury column length l, the temperature in degrees Celsius is:
t = [ (l − l₀) / (l₁₀₀ − l₀) ] × 100°C
To measure the temperature of an object, the thermometer bulb is held against it and allowed to reach thermal equilibrium. Once equilibrium is reached, the mercury column stops moving and its length directly tells us the temperature.
The Fahrenheit scale is another common system. In this scale, the ice point is 32°F and the steam point is 212°F. The conversion between Celsius and Fahrenheit is:
F = (9/5) × C + 32
A normal healthy human body temperature is around 98.6°F, which is 37°C on the Celsius scale.
5. Platinum Resistance Thermometer
Electrical resistance is another excellent thermometric property. The resistance of most metals increases with temperature. If we measure the resistance of a platinum wire at the ice point (R₀) and at the steam point (R₁₀₀), we can define temperature on the platinum scale as:
t = [ (Rₜ − R₀) / (R₁₀₀ − R₀) ] × 100°
The platinum resistance thermometer works on the principle of the Wheatstone bridge. In a Wheatstone bridge, four resistances P, Q, R, and X are arranged in a loop. A galvanometer is connected between two junction points. The bridge is said to be balanced (galvanometer reads zero) when:
P / Q = R / X
In the platinum resistance thermometer, the platinum coil is placed in the unknown temperature bath. Its resistance changes with temperature, and the bridge is adjusted by sliding a contact on a wire until balance is achieved. The position of this contact directly gives the temperature reading.
A compensating copper wire is also included in the setup. This compensates for the change in resistance of the connecting wires due to room temperature fluctuations, ensuring that only the platinum coil’s temperature change affects the reading.
Problem: The resistances of a platinum resistance thermometer at the ice point, steam point, and the boiling point of sulphur are 2.50 Ω, 3.50 Ω, and 6.50 Ω respectively. Find the boiling point of sulphur on the platinum scale.
Solution: Using the formula t = [(Rₜ − R₀) / (R₁₀₀ − R₀)] × 100°:
t = [(6.50 − 2.50) / (3.50 − 2.50)] × 100° = [4.00 / 1.00] × 100° = 400°
6. Constant Volume Gas Thermometer
Gas thermometers are more accurate than mercury or resistance thermometers for precise scientific work. In a constant volume gas thermometer, a fixed amount of gas is enclosed in a bulb. As temperature increases, the gas pressure increases while its volume is kept constant. This pressure is measured and used to define temperature.
The setup consists of a gas bulb connected through a capillary to a mercury manometer. A mercury reservoir can be raised or lowered to keep the gas at constant volume. The pressure of the gas is calculated as:
p = p₀ + hρg
Here, p₀ is atmospheric pressure, h is the difference in mercury levels in the manometer, ρ is the density of mercury, and g is gravitational acceleration.
For the centigrade scale on a gas thermometer, if p₀ is pressure at the ice point and p₁₀₀ is pressure at the steam point, the temperature corresponding to any pressure p is:
t = [ (p − p₀) / (p₁₀₀ − p₀) ] × 100°C
Problem: The pressure of air in the bulb of a constant volume gas thermometer is 73 cm of mercury at 0°C and 100.3 cm at 100°C. At room temperature, the pressure is 77.8 cm. Find the room temperature.
Solution: t = [(77.8 − 73) / (100.3 − 73)] × 100°C = [4.8 / 27.3] × 100°C ≈ 17°C
7. Ideal Gas Temperature Scale and the Kelvin
Here is a subtle but important problem: the temperature scales we have defined so far — mercury scale, platinum scale, gas scale — all depend on the properties of the specific substance used. Mercury and platinum do not expand or conduct electricity in exactly the same way as temperature changes. So their scales will give slightly different readings at the same physical state (except at the two fixed points where they are forced to agree).
We want a universal temperature scale that does not depend on any particular substance. Fortunately, such a scale exists. When experiments are done with different gases at lower and lower pressures (smaller and smaller amounts of gas), something remarkable happens: all gas thermometers agree with each other at any temperature. In the limit of zero pressure (ideal gas behaviour), gas thermometers become substance-independent.
This is the basis of the Ideal Gas Temperature Scale:
T = lim(pₜᵣ → 0) [ p / pₜᵣ ] × 273.16 K
The fixed reference point used here is the triple point of water — the unique temperature and pressure at which ice, liquid water, and water vapour can all coexist in equilibrium. This point is assigned the value 273.16 K (kelvin). Using a single fixed point (rather than two) is actually more accurate.
The unit kelvin (K) is the SI unit of thermodynamic temperature. The ideal gas temperature scale is identical to the absolute thermodynamic temperature scale — making it truly universal and substance-independent.
| Reference State | Kelvin (K) | Celsius (°C) | Fahrenheit (°F) |
|---|---|---|---|
| Absolute Zero | 0 K | −273.15°C | −459.67°F |
| Triple Point of Water | 273.16 K | 0.01°C | 32.02°F |
| Ice Point | 273.15 K | 0°C | 32°F |
| Steam Point | 373.15 K | 100°C | 212°F |
| Normal Body Temperature | 310.15 K | 37°C | 98.6°F |
8. The Celsius Scale and Its Relation to Kelvin
The Celsius scale (previously called the centigrade scale) is simply a shifted version of the Kelvin scale. The size of one degree Celsius is defined to be exactly the same as the size of one kelvin. The only difference is the starting point (zero point).
The Celsius scale is shifted from the Kelvin scale by exactly 273.15. So:
θ (°C) = T (K) − 273.15
This means 0°C = 273.15 K, and 100°C = 373.15 K. The term “centigrade” is now replaced by “Celsius” in official scientific usage. The Celsius scale is defined by the ideal gas scale, not by mercury expansion or platinum resistance, so it avoids the substance-dependence problem.
9. The Ideal Gas Equation
A key result that brings together pressure, volume, temperature, and amount of gas is the ideal gas equation. At low pressures and high temperatures (well above the condensation point of the gas), all gases obey this relationship very closely:
pV = nRT
Where: p = pressure, V = volume, n = number of moles, R = universal gas constant (8.314 J K⁻¹ mol⁻¹), T = absolute temperature in kelvin. A gas that obeys this equation exactly is called an ideal gas. Real gases behave like ideal gases when they are at low pressures and high temperatures.
10. Thermal Expansion: Linear, Area, and Volume
When most solid and liquid materials are heated, they expand. This is called thermal expansion. Understanding thermal expansion is critical in engineering — bridges, railways, and pipelines must all be designed to accommodate it.
Linear Expansion
For a solid rod of length L at temperature T, the coefficient of linear expansion α is defined as:
α = (1/L) × (dL/dT)
If α is small and approximately constant over a temperature range, then for a rod of length L₀ at 0°C, its length at temperature θ°C is:
Lθ = L₀ (1 + αθ)
Volume (Cubical) Expansion
For three-dimensional expansion, the relevant quantity is the coefficient of volume expansion γ:
γ = (1/V) × (dV/dT)
For an isotropic solid (one that expands equally in all directions), it can be shown mathematically that γ = 3α. The volume at temperature θ is:
Vθ = V₀ (1 + γθ)
Problem: An iron rod (50 cm) is joined end-to-end with an aluminium rod (100 cm) at 20°C. Find the composite length at 100°C. (α for iron = 12×10⁻⁶ °C⁻¹; α for aluminium = 24×10⁻⁶ °C⁻¹)
Iron at 100°C: 50 × [1 + 12×10⁻⁶ × 80] = 50.048 cm
Aluminium at 100°C: 100 × [1 + 24×10⁻⁶ × 80] = 100.192 cm
Composite length: 50.048 + 100.192 = 150.24 cm
Average α of composite rod: 0.24 / (150 × 80) = 20×10⁻⁶ °C⁻¹
Problem: A pendulum clock made of iron keeps correct time at 20°C. How much time does it lose or gain in 24 hours at 40°C? (α of iron = 1.2×10⁻⁵ °C⁻¹)
Concept: Time period T = 2π√(l/g). When temperature rises, the rod gets longer, the period increases, and the clock runs slow.
Fractional increase in period: ΔT/T = ½ × α × Δθ = ½ × 1.2×10⁻⁵ × 20 = 1.2×10⁻⁴
Time lost in 24 hours: 24 × 3600 × 1.2×10⁻⁴ ≈ 10.4 seconds
11. The Anomalous Expansion of Water
Water behaves differently from most substances in one important temperature range. Between 0°C and 4°C, water actually contracts as temperature increases. Its density reaches a maximum at 4°C. Above 4°C, water behaves normally and expands with increasing temperature.
When studying the expansion of a liquid in a container, you must also account for the expansion of the container itself. The volume that appears to overflow when a liquid is heated is the apparent expansion — the actual (real) expansion of the liquid minus the expansion of the container. The apparent coefficient of expansion γₐ = γ_liquid − γ_container.
12. Real-World Applications ofHeatHeat and Thermal Expansion
Understanding heat and temperature is not an academic exercise. These concepts power the modern world. Here are some areas where they matter deeply.
Structural Engineering: Steel bridges and railway tracks are built with expansion joints — small gaps that allow the metal to expand in summer without buckling. A steel rail that has no room to expand can warp dangerously.
Bimetallic Strips and Thermostats: Two metals with different coefficients of linear expansion are bonded together. When heated, one metal expands more than the other, causing the strip to bend. This bending can open or close an electrical circuit, which is the operating principle of a simple thermostat.
Fitting Metal Components: An iron ring with a slightly smaller diameter than a shaft can be heated until it expands enough to slide over the shaft. As it cools, it contracts and grips the shaft with enormous force. This technique is used in manufacturing engines and gear assemblies.
Medical Thermometers: Clinical mercury thermometers, digital resistance thermometers, and infrared ear thermometers all rely on thermometric properties — mercury expansion, resistance change, and infrared radiation respectively — to measure body temperature accurately.
Cooking and Food Science: Ovens, pressure cookers, and refrigerators all operate on principles rooted in thermal physics. Pressure cookers raise the boiling point of water by increasing pressure, cooking food faster. Refrigerators pump heat from a cold interior to the warm exterior using a refrigerant fluid.
13. Frequently Asked Questions
What is the difference between heat and temperature?
Temperature is a property of a body that measures how hot or cold it is — it is related to the average kinetic energy of the molecules. Heat is the energy that transfers between bodies due to a temperature difference. A body has a temperature; heat flows between bodies.
Why is the Zeroth Law called “zeroth” and not “first”?
The First and Second Laws of Thermodynamics were established before scientists recognised that there was a more fundamental law underlying them. Since this law had to come before the existing laws, it was numbered zero — hence the Zeroth Law.
Why do different thermometers give slightly different readings?
Because different thermometric substances (mercury, platinum, gas) do not change their properties at exactly the same rate as temperature changes. The scales are forced to agree at the ice point and steam point, but diverge in between. The ideal gas scale eliminates this by using the limiting behaviour of all gases at zero pressure.
What is absolute zero?
Absolute zero is the lowest possible temperature — 0 K, or −273.15°C. At absolute zero, a gas would have zero pressure and zero molecular motion. In practice, no substance can actually reach absolute zero, though scientists have come extremely close in laboratory conditions.
Why does water have maximum density at 4°C?
Water molecules form hydrogen bonds that create an open crystal-like structure when water is near freezing. Between 0°C and 4°C, these structures are breaking down as temperature rises, which causes the water to become more compact and dense. Above 4°C, normal thermal expansion takes over and density decreases as temperature increases.
What is the triple point of water and why is it used?
The triple point of water is the unique combination of temperature (0.01°C / 273.16 K) and pressure at which solid ice, liquid water, and water vapour can all coexist in equilibrium. It is used as the single fixed reference point for the Kelvin scale because it is highly reproducible and precisely defined — more accurate than using two separate fixed points like the ice point and steam point.
Heat is the non-mechanical transfer of energy between bodies at different temperatures. The Zeroth Law of Thermodynamics defines the concept of temperature and allows us to build thermometers. Different temperature scales exist — Celsius, Fahrenheit, and Kelvin — with Kelvin being the absolute scale that does not depend on any substance. Thermal expansion is the change in size of a body with temperature, with coefficients α (linear) and γ (volume) characterising how quickly different materials expand. Water is a unique exception that contracts between 0°C and 4°C — a property critical to aquatic life.
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