Specific Heat
Q = mcΔT and why water heats up so slowly
Do Now: On a sunny day at the beach, the sand burns your feet but the ocean water feels cool. They both got the same sunlight. Why?
Water has a much higher specific heat than sand. It takes far more energy to raise water’s temperature, so the same sunlight warms the sand much more.
A. Specific Heat
| Substance | Specific Heat, c (J/g•°C) |
|---|---|
| Water (liquid) | 4.18 |
| Aluminum | 0.90 |
| Iron | 0.45 |
| Copper | 0.39 |
High specific heat → temperature changes slowly (water). Low specific heat → temperature changes quickly (metals).
B. The Heat Equation
Heat Equation
Q = heat added or removed (J)
m = mass (g)
c = specific heat (J/g•°C)
ΔT = change in temperature = Tfinal − Tinitial (°C)
If Q comes out negative, the object lost energy (it cooled down).
C. Worked Examples
How much heat is needed to warm 250 g of water from 20. °C to 80. °C?
Given: m = 250 g, c = 4.18 J/g•°C, ΔT = 80. − 20. = 60. °C
Q = mcΔT = (250 g)(4.18 J/g•°C)(60. °C)
Q = 62,700 J (about 63 kJ)
A 500-g iron pan absorbs 9,000 J of heat. How much does its temperature rise?
Given: m = 500 g, c = 0.45 J/g•°C, Q = 9,000 J
ΔT = Qmc = 9,000 J(500 g)(0.45 J/g•°C)
ΔT = 40. °C
A 200-g sample of an unknown metal absorbs 1,800 J and its temperature rises 10. °C. What is the metal?
Given: m = 200 g, Q = 1,800 J, ΔT = 10. °C
c = QmΔT = 1,800 J(200 g)(10. °C) = 0.90 J/g•°C
From the table, the metal is aluminum.
D. Practice
How much heat does 100. g of water give off as it cools from 90. °C to 30. °C?
Q = (100.)(4.18)(−60.) = −25,080 J — about 25 kJ released.
A 50.-g piece of copper gains 975 J. How much does its temperature rise?
ΔT = 975 / (50. × 0.39) = 50. °C
How much energy does it take to heat 2.0 kg (2,000 g) of water from 15 °C to 100. °C for pasta?
Q = (2,000)(4.18)(85) = 710,600 J ≈ 711 kJ
A 300.-g metal block absorbs 2,700 J while warming by 20. °C. Identify the metal.
c = 2,700 / (300. × 20.) = 0.45 J/g•°C → iron
E. Specific Heat in the Real World
Coastal climates: oceans warm and cool slowly, so cities near the coast have milder temperatures.
Car radiators: water carries away lots of engine heat with only a small temperature rise.
Cookware: metal pots have low specific heat, so they heat up quickly.
Your body: mostly water, which helps keep your temperature steady.
Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. The same amount of heat is added to 100 g of water and 100 g of iron. Which has the larger temperature increase?
2. How much heat raises 10. g of water by 5.0 °C?
3. Why does the ocean stay cooler than the sand on a sunny day?
4. A 100.-g metal absorbs 390 J and warms by 10. °C. Its specific heat is
5. If Q is negative in Q = mcΔT, the object
Heating Water for Pasta
A cook heats 2000. g of water from 20. °C to its boiling point of 100. °C on a 1500-W electric burner. The specific heat of water is 4.2 J/g·°C.
Table 1: Specific Heats
| Substance | Specific Heat (J/g·°C) |
|---|---|
| Water | 4.2 |
| Aluminum | 0.90 |
| Iron | 0.45 |
| Copper | 0.39 |
How much thermal energy must be added to the water?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. Substitute numerical values into a mathematical representation that can be used to determine the time the 1500-W burner needs to heat the water to boiling, assuming all the burner’s energy goes into the water. Then calculate the time.
C2. Equal masses of water, aluminum, iron, and copper each absorb the same amount of energy. Which has the greatest temperature increase?
C3. The cook makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
C4. The burner runs for 2.0 minutes, and all of its energy goes into the 2000.-g of water starting at 20. °C. Determine the temperature of the water at that moment.
C5. At the beach on a sunny day, the sand becomes much hotter than the ocean water. Which explanation is best?
C6. When the cook timed the real burner, the water took about 600 s to boil instead of the predicted 450 s. Using energy reasoning, explain this difference, and describe one change to the cooking setup that would shorten the time.