What is Heat?

Heat is the transfer of thermal energy between objects due to a difference in temperature. It always flows from hot to cold until thermal equilibrium (equal temperature) is reached.

1. Heat Transfer Mechanisms

Heat can move in three ways:

MechanismMain IdeaMedium
ConductionDirect contactSolids (mostly)
ConvectionFluid movementLiquids and Gases
RadiationWavesVacuum and Transparent media

A. Conduction

Transfer through direct contact where particles vibrate and pass energy to neighbors. Metals are great conductors because they have "free electrons" that move energy quickly.

Curiosities & Examples of Conduction
  • Thermal Conductivity (k): A value that measures how fast heat moves. Copper (k=400) is much faster than wood (k=0.1).
  • The "Cold" Spoon: A metal spoon feels colder than a wooden one even if both are at 20°C because the metal conducts heat away from your hand faster.
  • Double Glazing: Windows use a layer of air between two glass panes. Since air is a terrible conductor, it keeps the house warm.

B. Convection

Transfer through the actual movement of a fluid (liquid or gas). Hot fluid expands, becomes less dense, and rises, while cold fluid sinks. This creates convection currents.

Curiosities & Examples of Convection
  • Sea Breezes: During the day, land heats up faster than the sea. Hot air over land rises, and cool air from the sea blows in to replace it.
  • Radiators: They are usually placed at the bottom of a room so the hot air can rise and circulate naturally.
  • Boiling Water: You can see "currents" in a pot as the hot water from the bottom moves up.

C. Radiation

Transfer via electromagnetic waves (mostly infrared). It is the only way heat can travel through a vacuum (like space).

Curiosities & Examples of Radiation
  • The Sun: We feel the Sun's heat even though there is 150 million km of empty space between us.
  • Colors: Black surfaces absorb radiation (and get hot), while white/shiny surfaces reflect it.
  • Night Vision: Thermal cameras "see" the infrared radiation emitted by warm bodies like humans or animals.

2. Specific Heat

To calculate the amount of energy (heat) required to change the temperature of an object, we use the following formula:

$$ E_q = m \cdot k_s \cdot \Delta T $$

Where:

  • Eh = Heat energy transferred (Joules, J)
  • m = Mass of the substance (kg)
  • ks = Specific heat capacity (J/kg·°C)
  • ΔT = Temperature change ($T_{final} - T_{initial}$)

Specific Heat Capacity (ks)

This is the energy required to raise the temperature of 1 kg of a substance by 1°C.

Specific Heat Capacity of common substances
Materialks (J/kg·°C)Why it matters
Water4 200Very high! Oceans stay cool in summer.
Ice2 100Half that of liquid water.
Aluminum900Good for pans.
Glass840Average insulator.
Iron450Heats up quickly.
Lead130Heats up extremely fast.

Worked Examples

Example 1: How much heat is needed to warm 2 kg of water from 20°C to 50°C? (ks = 4,200 J/kg·°C)

1. Identify data: m = 2 kg, $k_s = 4,200$, ΔT = 50 - 20 = 30°C

2. Apply formula: $E_q = 2 \times 4,200 \times 30$

3. Result: $E_q = 252,000 \text{ J}$

Example 2: An iron bar of 0.5 kg cools down from 100°C to 20°C. How much heat does it release? (ks = 450 J/kg·°C)

1. Identify data: m = 0.5 kg, $k_s = 450$, ΔT = 20 - 100 = -80°C

2. Apply formula: $E_q = 0.5 \times 450 \times (-80)$

3. Result: $E_q = -18,000 \text{ J}$ (Negative means energy is lost/released)

3. Latent heat (phase Changes)

State changes

When a substance changes state (like ice melting), it absorbs heat without changing its temperature.

$$ E_q = m \cdot k_l $$
  • kl = Latent heat (J/kg). For water fusion (melting), $k_l = 334,000 \text{ J/kg}$.
Example 3: How much heat is needed to melt 2 kg of ice at 0°C? (kl = 334,000 J/kg)

1. Identify data: m = 2 kg, $k_l = 334,000$

2. Apply formula: $E_q = 2 \times 334,000$

3. Result: $E_q = 668,000 \text{ J}$

4. Combined Calculations (Multi-step)

When a substance must be warmed to its melting point before it can melt, or warmed further after melting, we sum the heat from each step.

Example 4: Calculate the heat needed to turn 1 kg of ice at -10°C into water at 0°C (ks ice = 2,100 J/kg·°C, kl = 334,000 J/kg).

1. Step 1: Warm the ice to 0°C

$E_{q1} = 1 \text{ kg} \times 2,100 \times (0 - (-10)) = 21,000 \text{ J}$

2. Step 2: Melt the ice at 0°C

$E_{q2} = 1 \text{ kg} \times 334,000 = 334,000 \text{ J}$

3. Total: $E_{q1} + E_{q2} = 21,000 + 334,000 = \textbf{355,000 J}$

Example 5: – How much heat is needed to turn 0.2 kg of ice at -10°C into water at 50°C?

1. Step 1: Warm ice to 0°C: $E_{q1} = 0.2 \times 2,100 \times 10 = 4,200 \text{ J}$

2. Step 2: Melt ice at 0°C: $E_{q2} = 0.2 \times 334,000 = 66,800 \text{ J}$

3. Step 3: Warm water to 50°C: $E_{q3} = 0.2 \times 4,200 \times 50 = 42,000 \text{ J}$

4. Total: $4,200 + 66,800 + 42,000 = \textbf{113,000 J}$

1. Heat always flows... (1 points)

2. Why does a metal spoon feel colder than a wooden spoon at the same room temperature? (1 points)

3. How does the Sun's heat reach Earth? (1 points)

4. In a convection current, hot fluid rises because: (1 points)

5. What does specific heat capacity (k_s) represent? (1 points)

6. What does latent heat (k_l) represent? (1 points)

7. Which substance requires the most energy to heat 1 kg by 1°C? (1 points)

8. During a phase change (e.g., ice melting at 0°C), what happens to the temperature? (1 points)

9. How much heat is needed to warm 2 kg of water from 20°C to 50°C? (k_s = 4,200 J/kg·°C) (1 points)

10. An iron bar (m = 0.5 kg, k_s = 450 J/kg·°C) cools from 100°C to 20°C. How much heat does it release? (1 points)

11. How much heat is needed to warm 3 kg of aluminum (k_s = 900 J/kg·°C) from 25°C to 85°C? (1 points)

12. How much heat is needed to warm 0.2 kg of lead (k_s = 130 J/kg·°C) from 20°C to 120°C? (1 points)

13. 9,000 J is added to 1 kg of iron (k_s = 450 J/kg·°C). By how much does its temperature increase? (1 points)

14. 42,000 J warms a sample of water (k_s = 4,200 J/kg·°C) by 10°C. What is the mass of the water? (1 points)

15. 2 kg of water at 100°C is cooled to 20°C (k_s = 4,200 J/kg·°C). How much heat is released? (1 points)

16. How much heat is needed to melt 2 kg of ice at 0°C? (k_l = 334,000 J/kg) (1 points)

17. How much heat is released when 0.5 kg of water freezes at 0°C? (k_l = 334,000 J/kg) (1 points)

18. 1,002,000 J of heat is used to melt ice at 0°C (k_l = 334,000 J/kg). How many kilograms melted? (1 points)

19. How much total heat is needed to convert 0.1 kg of ice at 0°C into water at 20°C? (k_l = 334,000 J/kg, k_s(water) = 4,200 J/kg·°C) (1 points)

20. k_s Calculation Practice: (4 points)

a ) Warm 0.5 kg of aluminum (k_s = 900 J/kg·°C) from 20°C to 60°C. E_q = _____ J

b ) How much heat does 2 kg of water (k_s = 4,200 J/kg·°C) release when cooling from 80°C to 30°C? (positive number) E_q = _____ J

c ) A glass cup (m = 0.3 kg, k_s = 840 J/kg·°C) warms from 15°C to 65°C. E_q = _____ J

d ) 50,400 J warms 4 kg of iron (k_s = 450 J/kg·°C). The temperature increase is ΔT = _____ °C

21. Latent Heat (k_l) Practice: (3 points)

a ) How much heat is needed to melt 3 kg of ice at 0°C? (k_l = 334,000 J/kg) E_q = _____ J

b ) 835,000 J is used to melt ice at 0°C (k_l = 334,000 J/kg). How many kg melted? m = _____ kg

c ) How much heat is released when 1.5 kg of water at 0°C freezes? (k_l = 334,000 J/kg) E_q = _____ J

22. Step-by-step: 1 kg of ice from −10°C to liquid water at 0°C (3 points)

a ) Step 1 — Warm 1 kg of ice from −10°C to 0°C (k_s(ice) = 2,100 J/kg·°C). E_q1 = _____ J

b ) Step 2 — Melt that 1 kg of ice at 0°C (k_l = 334,000 J/kg). E_q2 = _____ J

c ) Total heat for both steps. E_q(total) = _____ J

23. Step-by-step: 0.2 kg of ice from −10°C to water at 50°C (4 points)

a ) Step 1 — Warm 0.2 kg of ice from −10°C to 0°C (k_s(ice) = 2,100 J/kg·°C). E_q1 = _____ J

b ) Step 2 — Melt 0.2 kg of ice at 0°C (k_l = 334,000 J/kg). E_q2 = _____ J

c ) Step 3 — Warm 0.2 kg of water from 0°C to 50°C (k_s(water) = 4,200 J/kg·°C). E_q3 = _____ J

d ) Total heat for all three steps. E_q(total) = _____ J

24. Step-by-step: 0.5 kg of ice from −20°C to water at 40°C (4 points)

a ) Step 1 — Warm 0.5 kg of ice from −20°C to 0°C (k_s(ice) = 2,100 J/kg·°C). E_q1 = _____ J

b ) Step 2 — Melt 0.5 kg of ice at 0°C (k_l = 334,000 J/kg). E_q2 = _____ J

c ) Step 3 — Warm 0.5 kg of water from 0°C to 40°C (k_s(water) = 4,200 J/kg·°C). E_q3 = _____ J

d ) Total heat for all three steps. E_q(total) = _____ J