SME
Grade 10 Science · Problem type
Heat to turn ice into steam
Use this for the heat to take ice all the way to steam: warm it to 0 °C, melt it, warm the water to 100 °C and boil it away.
Chart
Melting point = 0 °C
Boiling point = 100 °C
Heat added = 209 + 3,340 + 4,180 + 22,600 = 30,329 J
Mass of water: 10 g
Total heat: 30,329 J
This is an example. Type your own values to start a new problem.
m
Mass of water
example · g
T₀
Starting temperature of the ice
example · °C
q₁
Heat to warm the ice to 0 °C
calculated · J
q₂
Heat to melt the ice
calculated · J
q₃
Heat to warm the water to 100 °C
calculated · J
q₄
Heat to boil the water
calculated · J
q
Total heat
calculated · J
Formulas
q₁
=
m
×
2.09
×
(0
−
T₀
)
209 = 10 × 2.09 × (0 − (−10))
q₂
=
m
×
334
3,340 = 10 × 334
q₃
=
m
×
4.18
×
100
4,180 = 10 × 4.18 × 100
q₄
=
m
×
2,260
22,600 = 10 × 2,260
q
=
q₁
+
q₂
+
q₃
+
q₄
30,329 = 209 + 3,340 + 4,180 + 22,600
Assumptions
•
Ice 2.09, water 4.18 J/(g·°C); melting takes 334 J/g and boiling 2260 J/g.
•
While ice melts or water boils, the temperature stays flat: the heat breaks attractions instead.
Step-by-step
WE KNOW
m = 10 g, T₀ = −10 °C
FIND
heat to warm the ice to 0 °C (q₁), heat to melt the ice (q₂), heat to warm the water to 100 °C (q₃), heat to boil the water (q₄), total heat (q)
Step 1 · Find heat to warm the ice to 0 °C (q₁)
Use q₁ = m × 2.09 × (0 − T₀)
Ice warms from its start to 0 °C at 2.09 J for each gram and degree.
q₁
=
10
×
2.09
×
(0
−
(−10))
q₁
=
10
×
2.09
×
10
q₁
=
20.9
×
10
q₁
=
209
J
Step 2 · Find heat to melt the ice (q₂)
Use q₂ = m × 334
Melting takes 334 J for each gram, at 0 °C.
q₂
=
10
×
334
q₂
=
3,340
J
Step 3 · Find heat to warm the water to 100 °C (q₃)
Use q₃ = m × 4.18 × 100
Water warms by 100 °C, at 4.18 J for each gram and degree.
q₃
=
10
×
4.18
×
100
q₃
=
41.8
×
100
q₃
=
4,180
J
Step 4 · Find heat to boil the water (q₄)
Use q₄ = m × 2,260
Boiling takes 2260 J for each gram, at 100 °C.
q₄
=
10
×
2,260
q₄
=
22,600
J
Step 5 · Find total heat (q)
Use q = q₁ + q₂ + q₃ + q₄
Add the heat of the four stages.
q
=
209
+
3,340
+
4,180
+
22,600
q
=
30,329
J
Check
Put the numbers back in. Both sides should match.
209 = 10 × 2.09 × (0 − (−10)) ✓
3,340 = 10 × 334 ✓
4,180 = 10 × 4.18 × 100 ✓
22,600 = 10 × 2,260 ✓
30,329 = 209 + 3,340 + 4,180 + 22,600 ✓
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