Interactive thermal energy & thermodynamics laboratory
Heat
Explore the dynamics of heat as thermal energy in transit. Interact with three simulations: compare conduction, convection, and radiation side-by-side; map latent heat on a phase-change heating curve; or drop weights to measure Joule's mechanical equivalent of heat.
Thermal Physics Lab Setup
Select a mode above. Heat materials to trace conduction paths, convection loops, and radiational absorption. Melt ice to plot latent flat steps, or drop Joule's mass weights to churn potential energy into water temperature rise.
Live Lab Telemetry
- Temperature
- 20.0 °C
- Heat Flow Rate
- 0.0 W
- Work Input (W)
- 0.0 J
- Heat Yield (Q)
- 0.0 cal
- Joule's Ratio (W/Q)
- ---
- Physical State
- Solid Ice
What is Heat?
In physics, heat (symbol: \(Q\)) is defined as the spontaneous flow of thermal energy from one body or thermodynamic system to another due to a difference in their temperatures. Heat is a **path function**—it is energy in transit, meaning a substance does not "contain" heat. Instead, an object possesses **internal energy** (the combined kinetic and potential energies of its microscopic particles), and heat is simply the mechanism of energy transfer across boundaries.
Historically, heat was thought to be an weightless fluid called caloric that flowed between bodies. This theory was disproved by Benjamin Thompson (Count Rumford) and James Prescott Joule, who established the mechanical equivalence of heat.
Modes of Heat Transfer
Heat propagates through three distinct physical mechanisms:
- Conduction: Direct contact molecular collisions. Energy transfers from high-amplitude vibrating particles to neighbors without net mass motion.
- Convection: Fluid current cycles. Warm fluid expands, density decreases, causing it to float upward while colder, denser fluid sinks.
- Radiation: Energy emitted as electromagnetic waves (chiefly infrared). Does not require physical media to propagate.
Fundamental Equations
\(Q_{\text{sensible}} = m c \Delta T\)
\(Q_{\text{latent}} = m L\)
\(Q/t = k A \Delta T / d \quad \text{ (Conduction)}\)
\(P = \sigma e A T^4 \quad \text{ (Radiation)}\)
Heat vs Temperature vs Internal Energy
| Property | Heat (Q) | Temperature (T) | Internal Energy (U) |
|---|---|---|---|
| Definition | Energy in transit across systems | Average molecular kinetic energy | Total atomic energy sum |
| SI Unit | Joule (J) | Kelvin (K) | Joule (J) |
| State Variable? | No (Path function) | Yes (State function) | Yes (State function) |
Latent Heat Phase Changes
During a phase change, heat is added or removed without any temperature change. This energy is used to break or form intermolecular bonds:
- Latent Heat of Fusion (\(L_f\)): Transition between solid and liquid phases. For water, \(L_f \approx 3.34 \times 10^5\text{ J/kg}\).
- Latent Heat of Vaporization (\(L_v\)): Transition between liquid and gas phases. For water, \(L_v \approx 2.26 \times 10^6\text{ J/kg}\).
Solved Examples
Calculate the total heat required to convert 0.5 kg of ice at -10°C to liquid water at 20°C. (Specific heat of ice = 2100 J/(kg·K), Specific heat of water = 4184 J/(kg·K), Latent heat of fusion = 3.34 × 10<sup>5</sup> J/kg)
- The process occurs in three stages: heating the ice, melting the ice, and heating the water.
- Stage 1: Heat ice from -10°C to 0°C: \(Q_1 = m c_{\text{ice}} \Delta T = 0.5 \times 2100 \times (0 - (-10)) = 10,500\text{ J}\).
- Stage 2: Melt ice at 0°C: \(Q_2 = m L_f = 0.5 \times 3.34 \times 10^5 = 167,000\text{ J}\).
- Stage 3: Heat liquid water from 0°C to 20°C: \(Q_3 = m c_{\text{water}} \Delta T = 0.5 \times 4184 \times (20 - 0) = 41,840\text{ J}\).
- Total heat required: \(Q_{\text{total}} = Q_1 + Q_2 + Q_3 = 10,500 + 167,000 + 41,840 = 219,340\text{ J}\).
Answer: Total Heat = 219,340 J (or 219.34 kJ)
In a mechanical equivalent of heat lab (Joule's apparatus), two 5 kg weights fall through a height of 2.0 m, spinning a paddle wheel in a container holding 0.25 kg of water. If the weights fall 20 times, calculate the total mechanical work done and the theoretical temperature rise of the water, neglecting heat capacity of the container. (Assume g = 9.8 m/s²)
- Calculate mechanical work done: \(W = N \times (2 m g h)\), where \(N = 20\) falls.
- Substitute values: \(W = 20 \times 2 \times 5\text{ kg} \times 9.8\text{ m/s}^2 \times 2.0\text{ m} = 3920\text{ Joules}\).
- Convert work to equivalent heat generated using Joule's constant (1 cal = 4.184 J): \(Q = W / 4.184 = 3920 / 4.184 \approx 936.9\text{ calories}\).
- Use the heat equation to find temperature rise \(\Delta T\): \(W = m_{\text{water}} c_{\text{water}} \Delta T\) where \(c_{\text{water}} = 4184\text{ J/(kg\cdot K)}\).
- Solve for \(\Delta T\): \(\Delta T = W / (m c) = 3920 / (0.25 \times 4184) = 3920 / 1046 \approx 3.75^\circ\text{C}\).
Answer: Work = 3920 J, Temperature Rise ΔT ≈ 3.75°C
A double-pane glass window consists of two glass sheets, each 0.8 m × 1.2 m and 4.0 mm thick, separated by a 10 mm air gap. The indoor temperature is 20°C and outdoor is -5°C. Calculate the heat conduction rate. (Thermal conductivity of glass = 0.8 W/(m·K), air = 0.026 W/(m·K))
- The thermal resistance \(R_t\) of a composite wall is the sum of individual resistances: \(R_{\text{total}} = R_{\text{glass1}} + R_{\text{air}} + R_{\text{glass2}}\).
- For a single layer, \(R = d / (k A)\) where \(A = 0.8 \times 1.2 = 0.96\text{ m}^2\).
- Calculate resistances: \(R_{\text{glass}} = 0.004 / (0.8 \times 0.96) \approx 0.0052\text{ K/W}\).
- Calculate air gap resistance: \(R_{\text{air}} = 0.010 / (0.026 \times 0.96) \approx 0.4006\text{ K/W}\).
- Total resistance: \(R_{\text{total}} = 0.0052 + 0.4006 + 0.0052 = 0.411\text{ K/W}\).
- Heat transfer rate: \(Q/t = \Delta T / R_{\text{total}} = (20 - (-5)) / 0.411 = 25 / 0.411 \approx 60.8\text{ Watts}\).
Answer: Conduction Rate = 60.8 W
Common Mistakes
- Saying an object "has heat". Objects possess internal energy, not heat. Heat is energy in transit.
- Adding temperature rise during phase change calculations. While ice is melting or water is boiling, temperature remains constant.
- Confusing the calorie (4.184 J) with the dietary Calorie (1 kcal = 1000 cal = 4184 J).
- Thinking thermal radiation requires air or media. Radiation travels through empty vacuums (like sunlight).
Practice Questions
1. What distinguishes heat from internal energy?
Internal energy is the total kinetic and potential energy of all molecules in a substance. Heat is only the energy that is transferred from one object to another due to a temperature difference.
2. Why do metal handles on cooking pots feel hotter than wooden handles at the same temperature?
Metals are excellent thermal conductors with high thermal conductivity (k). They transfer heat to your hand much faster than wood, which is a thermal insulator.
3. Explain how double-walled vacuum flasks (thermoses) prevent all three modes of heat transfer.
The vacuum between the double walls eliminates conduction and convection (no medium particles). Silvered surfaces reflect infrared radiation back inside, minimizing radiation losses.
4. How much heat is released when 100 g of steam at 100°C condenses to water at 100°C?
Using latent heat of vaporization: \(Q = m L_v = 0.1\text{ kg} \times (2.26 \times 10^6\text{ J/kg}) = 226,000\text{ J} = 226\text{ kJ}\).
Quick Summary
- Heat is the transfer of thermal energy due to a temperature gradient.
- It propagates via conduction (solids), convection (fluids), and radiation (electromagnetic waves).
- Sensible heat changes temperature (\(Q = mc\Delta T\)), while latent heat changes phase (\(Q = mL\)).
- Joule's mechanical equivalent established that mechanical work can convert completely into heat (\(1\text{ cal} \approx 4.18\text{ J}\)).
Frequently Asked Questions
What is heat in simple terms?
Heat is thermal energy in transit. It is the energy that moves spontaneously from a warmer object to a cooler one because of their difference in temperature.
Can a substance "contain" heat?
No. Objects contain internal energy (molecular kinetic and potential energy), but they do not contain heat. Heat only exists when energy is in the process of transferring between substances.
Why is water used as a coolant in car radiators?
Water has a very high specific heat capacity (4184 J/kg·K), meaning it can absorb a large amount of heat energy with only a small increase in its own temperature.
What is latent heat of vaporization?
It is the amount of heat energy needed to change a substance from liquid to gas at its boiling point without raising its temperature.
What is the mechanical equivalent of heat?
It is the conversion factor that shows work and heat are different forms of the same physical quantity (energy). Specifically, 1 calorie of heat equals about 4.184 Joules of mechanical work.
How does heat travel through a vacuum?
Through radiation. Hot objects emit electromagnetic infrared waves, which travel through empty space at the speed of light and turn back into thermal energy when absorbed by another object.
What is the difference between natural and forced convection?
Natural convection is driven by buoyancy forces (hot fluid rises because it expands and becomes less dense). Forced convection uses external devices like fans or pumps to move the heated fluid.
What is absolute zero?
Absolute zero (-273.15°C or 0 K) is the lowest possible temperature, where all classical random thermal motion of particles ceases.
What is a calorie?
A calorie is a non-SI unit of energy. It is the amount of heat needed to raise the temperature of 1 gram of water by 1°C. 1 calorie is equal to 4.184 Joules.
Why does perspiration (sweating) cool our bodies?
Sweat is liquid water on our skin. As it evaporates into gas, it absorbs the latent heat of vaporization from our bodies, cooling us down.