SME
Grade 11 Science · Problem type
Heat to warm something: Q = mcΔT
Use this for “How much heat warms 2 kg of water from 15 °C to 65 °C?”
Diagram
Heat taken in by the water: q = mcΔT = 2 × 4,180 × 50 = 418,000 J
The water warmed: the reaction gave off 418,000 J.
Exothermic.
This is an example. Type your own values to start a new problem.
Q (J)
=
m (kg)
×
c (J/(kg·°C))
×
(
T₂ (°C)
−
T₁ (°C)
)
ΔT
Change in temperature
calculated · °C
Formulas
ΔT
=
T₂
−
T₁
50 = 65 − 15
Q
=
m
×
c
×
ΔT
418,000 = 2 × 4,180 × 50
Assumptions
•
The specific heat c is the heat that warms 1 kg by 1 °C: water 4,180 J/(kg·°C), aluminum 900, iron 450, copper 385.
•
Nothing melts or boils between T₁ and T₂.
•
A negative Q means heat was given off as it cooled.
Step-by-step
WE KNOW
m = 2 kg, c = 4,180 J/(kg·°C), T₁ = 15 °C, T₂ = 65 °C
FIND
change in temperature (ΔT), heat (Q)
Step 1 · Find change in temperature (ΔT)
Use ΔT = T₂ − T₁
The change is the final temperature less the first.
ΔT = 65 − 15
ΔT = 50 °C
Step 2 · Find heat (Q)
Use Q = m × c × ΔT
Heat is the mass times the specific heat times the change in temperature.
Q
=
2
×
4,180
×
50
Q
=
8,360
×
50
Q
=
418,000
J
Check
Put the numbers back in. Both sides should match.
50 = 65 − 15 ✓
418,000 = 2 × 4,180 × 50 ✓
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