This unit is about what happens to energy when things heat up, cool down, melt, or boil. By the end, you should be able to tell temperature, thermal energy, and heat apart, and calculate how much energy it takes to change an object's temperature or phase.
Read the overview first, then work through each topic's notes and try the checkpoint question before checking the answer.
Earlier units tracked kinetic and potential energy of whole objects. This unit zooms in to the particles inside an object and the energy associated with their motion and interactions. Energy conservation still runs the show, and it now includes heat.
Honors Physics Unit 11 covers thermal physics. You'll learn the difference between temperature and thermal energy, convert between Celsius, Fahrenheit, and Kelvin, and use Q = mcΔT with specific heat to find energy transfers and final temperatures in mixing (calorimetry) problems. You'll compare conduction, convection, and radiation. You'll also use Q = mL with latent heats of fusion and vaporization for phase changes at constant temperature. For a pure substance at constant pressure, temperature stays flat during melting or boiling. Many courses connect this to the first law of thermodynamics, ΔU = Q + W, where W is work done on the system.
A bathtub of 40°C water and a cup of 40°C water have the same temperature, but the bathtub has more thermal energy because it contains more water. For an ideal gas, temperature in kelvins is directly proportional to the average translational kinetic energy of its particles.
An object doesn't contain heat. It contains thermal energy, and heat is the name for the energy that crosses between objects at different temperatures. Heat can be transferred by conduction, convection, or radiation. At thermal equilibrium, there is no net heat transfer between the objects.
For heating within a single phase, Q = mcΔT relates heat transfer to temperature change when specific heat is approximately constant and other energy transfers are negligible. For a pure substance melting or boiling at constant pressure, temperature stays constant while energy changes the arrangement and interactions of particles. Use Q = mL for that phase change. A heating curve shows these processes as sloped and flat segments.
Every problem in this unit is an energy bookkeeping problem. If two objects exchange heat only with each other, heat lost by the hot object equals heat gained by the cold one. For a closed system, the first law is ΔU = Q + W, where Q is heat added and W is work done on the system. If you track where every joule goes, the formulas follow.
Temperature describes how hot or cold a substance is.
Heat (Q) is energy transferred because of a temperature difference.
When a pure substance melts or boils at constant pressure, its temperature stays constant during the phase change.
Temperature describes how hot or cold a substance is. For an ideal gas, it is proportional to the average translational kinetic energy of the particles. Thermal energy includes energy associated with particle motion and interactions. A lake at 20°C has much more thermal energy than a cup of water at 100°C, even though the cup is hotter, because the lake has vastly more particles.
For an ideal gas, the average translational kinetic energy per particle is , where J/K and is in kelvins. Use kelvins because this formula requires absolute temperature. Doubling the Kelvin temperature doubles that average kinetic energy. Doubling a Celsius reading does not. Absolute zero is 0 K, although quantum systems can still have zero-point motion.
Use these conversions:
A kelvin and a Celsius degree are the same size, so a temperature change of 10°C is also a change of 10 K. A Fahrenheit degree is smaller, so a 10°C change is an 18°F change.
When two objects at different temperatures touch, heat flows from the hotter one to the colder one. If they exchange energy only with each other, they reach the same temperature and thermal equilibrium. The zeroth law says that if A and B are each in equilibrium with C (say, a thermometer), then A and B are in equilibrium with each other, which is why thermometers work.
Check yourself: An ideal gas is heated from 27°C to 327°C. By what factor does the average translational kinetic energy of its particles increase? (Answer: Convert to kelvins first, giving 300 K and 600 K. The Kelvin temperature doubles, so the average kinetic energy doubles. It does not increase by a factor of about 12.)
| Quantity | What it describes | Depends on amount of material? | Units |
|---|---|---|---|
| Temperature | How hot or cold a system is | No | K, °C, °F |
| Thermal energy | Energy associated with particle motion and interactions | Yes | J |
| Heat | Energy transferred because of a temperature difference | Yes | J |
Heat () is energy transferred because of a temperature difference. It's measured in joules, and 1 cal = 4.184 J. Specific heat () is the energy needed to raise 1 kg of a material by 1°C. Water's is high, about 4186 J/(kg·°C), so it warms and cools slowly. Metals like iron (about 450 J/(kg·°C)) change temperature quickly.
For heating or cooling without a phase change, applies when specific heat is approximately constant and other energy transfers are negligible. A positive means heat entered the object, and a negative means heat left it.
Worked example. A 0.200 kg iron block at 90°C is dropped into 0.500 kg of water at 20°C. Find the final temperature . In an isolated system, heat lost by the iron equals heat gained by the water. Set up . This becomes . Rearranging gives , so °C. The water barely warms because of its large mass and specific heat.
Heat moves in three ways. Conduction transfers energy through interactions between neighboring particles and, in metals, through mobile electrons. For steady conduction through a uniform slab, the rate is , where is conductivity, is area, and is thickness. Convection carries energy by moving fluid, as when hot air rises. Radiation sends energy as electromagnetic waves, even through a vacuum.
Check yourself: How much heat does it take to warm 2.0 kg of water from 15°C to 65°C? (Answer: Q = mcΔT = (2.0)(4186)(50) = 418,600 J, or about 419 kJ.)
| Method | How energy moves | Needs a medium? | Everyday example |
|---|---|---|---|
| Conduction | Particle interactions and, in metals, mobile electrons | Yes, works best in solids | A metal spoon getting hot in soup |
| Convection | Bulk flow of a heated fluid | Yes, liquids and gases only | Warm air rising from a heater |
| Radiation | Electromagnetic waves | No, works in a vacuum | Sunlight warming Earth |
When a pure substance melts or boils at constant pressure, its temperature stays constant during the phase change. The energy changes the arrangement and interactions of its particles. Latent heat is the energy transferred per unit mass. Use for heat absorbed and for heat released, with positive.
At about 1 atm, water's latent heat of fusion is J/kg at 0°C, and its latent heat of vaporization is J/kg at 100°C. Vaporization requires much more energy per kilogram than melting because particles become much more widely separated. Steam at 100°C can cause a more severe burn than water at 100°C because it releases energy when it condenses on skin.
Melting and vaporization absorb energy. Freezing and condensation release the same amount for the same mass at the same phase-change conditions.
Worked example. How much energy turns 0.100 kg of ice at -10°C into water at 20°C? Use J/(kg·°C). Step 1, warm the ice: J. Step 2, melt it: J. Step 3, warm the water: J. The total is about 43,900 J. Melting takes most of the energy.
On a heating curve for a pure substance at constant pressure, sloped segments can use and phase-change plateaus use .
Check yourself: How much energy is released when 0.050 kg of steam at 100°C condenses into water at 100°C? (Answer: The energy released has magnitude mL_v = (0.050)(2.26 × 10^6) = 113,000 J, so Q = -113,000 J for the steam. The temperature stays at 100°C the whole time.)
| Term | Definition |
|---|---|
| Temperature | A measure of the average kinetic energy of the particles in a substance. |
| Thermal energy | Energy associated with particle motion and interactions in an object. |
| Heat | Energy transferred between objects because of a temperature difference, always flowing from hot to cold on its own. |
| Specific heat capacity | The energy needed to raise 1 kg of a material by 1°C, used in Q = mcΔT. |
| Latent heat | Energy per kilogram absorbed or released during a phase change at constant temperature, used in Q = mL. |
| Conduction | Heat transfer through interactions between neighboring particles and, in metals, through mobile electrons. |
| Convection | Heat transfer by the bulk movement of a heated liquid or gas. |
| Radiation | Heat transfer by electromagnetic waves, which needs no medium and can cross a vacuum. |
| Kelvin scale | An absolute temperature scale that starts at absolute zero and has degrees the same size as Celsius degrees. |
| First law of thermodynamics | For a closed system, the rule that internal energy changes by the heat added plus the work done on the system, written ΔU = Q + W. |
Everyday language says something "has a lot of heat," which blurs the two ideas. In physics, temperature describes how hot or cold a system is, and heat is energy transferred because of a temperature difference. Ask yourself whether the problem is asking how hot something is or how much energy moved.
The ideal-gas formula requires absolute temperature in kelvins. For a temperature change ΔT in Q = mcΔT, Celsius and Kelvin give the same number, so either works there. Check what temperature scale a formula requires before substituting.
For a pure substance melting or boiling at constant pressure, ΔT is zero during the phase change, but energy is still transferred. Split the process into steps. Use mcΔT for each warming or cooling stretch and mL for each phase-change plateau, then add the pieces with their signs.
If you write ΔT as final minus initial for both objects, the hot object's Q comes out negative. If the two objects exchange energy only with each other, then Q_hot + Q_cold = 0. Alternatively, write heat lost = heat gained and use positive temperature differences on each side. Pick one method and stick with it. Mixing the two methods is how sign errors happen.