Metal Specific Heat Calculator: Heat From q = mcΔT

This calculator finds the heat needed to warm a piece of metal, or the heat it gives off as it cools. Choose the metal, enter the mass in grams and the starting and final temperatures; you get the heat q in joules, kilojoules and calories.

Formula

q = m × c × ΔT, with ΔT = T_final − T_start.

• q: heat in joules (J); positive when the metal absorbs heat, negative when it releases it
• m: mass in grams
• c: specific heat capacity in J/(g·°C), near 25 °C: aluminium 0.897, copper 0.385, iron 0.449, silver 0.235, lead 0.129, zinc 0.388
• ΔT: temperature change; a change of 1 °C equals a change of 1 K
• 1 cal = 4.184 J (thermochemical calorie)

Worked Example

Heating 100 g of aluminium from 20 °C to 75 °C.

1. ΔT = 75 − 20 = 55 °C
2. q = 100 × 0.897 × 55 = 4,933.5 J
3. In kilojoules: 4,933.5 ÷ 1000 = 4.9335 kJ
4. In calories: 4,933.5 ÷ 4.184 = 1,179.1 cal

Assumptions

• The specific heat is constant over the temperature range; for metals this holds well between about 0 and 100 °C.
• No phase change occurs between the two temperatures (no melting).
• The metal is pure; alloys such as brass or steel have their own values.
• No heat is lost to the surroundings or to a container.

How to read the result

A positive q is the energy the metal takes up; a negative q (final temperature lower than start) is the energy it gives to its surroundings, for example the water in a calorimeter. Metals with a low specific heat, such as lead, change temperature quickly for little energy; aluminium needs about seven times more energy per gram than lead for the same rise.

Limits and common mistakes

• Using kelvin for one temperature and °C for the other: the difference must use one scale.
• Entering the mass in kilograms with c in J/(g·°C) gives an answer 1000 times too small.
• Mixing J/(g·°C) and J/(kg·K): 0.897 J/(g·°C) = 897 J/(kg·K).
• In a calorimetry experiment, heat lost by the metal equals heat gained by the water only if the container and losses are accounted for.

Frequently Asked Questions

What is the specific heat of aluminium?

About 0.897 J/(g·°C) near room temperature.

How much heat does 100 g of aluminium need to warm by 55 °C?

About 4,933.5 J, or 4.93 kJ.

Why is my answer negative?

The final temperature is below the starting one, so the metal released heat.

How do I find the specific heat of an unknown metal?

Rearrange to c = q ÷ (m × ΔT), using the heat measured in a calorimeter.

sel c | Metal (specific heat in J/(g·°C)) | Aluminium 0.897=0.897, Copper 0.385=0.385, Iron 0.449=0.449, Silver 0.235=0.235, Lead 0.129=0.129, Zinc 0.388=0.388
in m | Mass of the metal | g | 100 | 0
in t1 | Starting temperature | °C | 20 | -273.15
in t2 | Final temperature | °C | 75 | -273.15
out q | Heat absorbed (negative = released) | J | m * c * (t2 - t1) | 1
out kj | Heat in kilojoules | kJ | q / 1000 | 4
out cal | Heat in calories | cal | q / 4.184 | 1