The specific heat equation (q = mcΔT) calculates heat energy transferred during temperature changes. It's essential for calorimetry, thermodynamics, and understanding how substances store thermal energy.
q = mcΔT
Heat = mass × specific heat × temperature change
Units: J (joules), kJ (kilojoules), cal (calories)
Amount of thermal energy transferred
• Positive q = heat absorbed (endothermic)
• Negative q = heat released (exothermic)
Units: g (grams) or kg (kilograms)
Amount of substance being heated or cooled
Units: J/(g·°C) or J/(g·K)
Heat needed to raise 1 gram by 1°C
💡 Unique property of each substance
Units: °C or K (same magnitude)
Formula: ΔT = Tfinal - Tinitial
• Positive ΔT = temperature increase
• Negative ΔT = temperature decrease
| Substance | c [J/(g·°C)] | Notes |
|---|---|---|
| Water | 4.184 | Highest of common liquids |
| Ice | 2.09 | Solid H₂O |
| Steam | 2.01 | Water vapor |
| Aluminum | 0.897 | Metal |
| Iron | 0.449 | Metal |
| Copper | 0.385 | Metal |
| Gold | 0.129 | Metal (low c) |
| Ethanol | 2.44 | Liquid alcohol |
💡 Water has an unusually high specific heat - it takes lots of energy to heat water!
q = mcΔT
m = q / (cΔT)
c = q / (mΔT)
ΔT = q / (mc)
ΔT = Tfinal - Tinitial = 80°C - 20°C = 60°C
q = mcΔT
q = (250 g)(4.184 J/g·°C)(60°C)
q = 62,760 J = 62.8 kJ
Answer: 62.8 kJ of heat energy needed
Positive q means heat must be added to raise temperature.
ΔT = final - initial, NOT initial - final. Sign matters! Heating gives positive ΔT, cooling gives negative.
If c is in J/(g·°C), mass must be in grams and ΔT in °C. If c is in J/(kg·K), use kg and K.
Ice, water, and steam have different specific heats! Use the correct value for the substance's state.
q = mcΔT is for temperature changes ONLY. Phase changes (melting, boiling) use q = mΔH instead.
Specific heat (c) is the energy needed to raise 1 gram of a substance by 1°C. It's a property unique to each material.
Hydrogen bonding in water requires lots of energy to break. This makes water an excellent temperature buffer and coolant.
Yes! A change of 1°C equals a change of 1 K, so ΔT has the same numerical value in both units.
Lowercase q is typically heat transfer, uppercase Q sometimes represents total heat or charge. Context matters, but both can represent heat.
Specific heat (c) is per gram. Heat capacity (C) is for the entire object: C = mc. If you know the total mass, C = total heat per degree.