Let’s solve each problem step by step using the formulas provided in the worksheet.
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Formula Reminder:
- For temperature change (no phase change):
Q = mass × ΔT × specific heat capacity
where ΔT = Final Temp – Initial Temp
- For phase change (melting/freezing or vaporization/condensation):
Q = mass × heat of fusion (or vaporization)
> Note: “Given off” means heat is released → Q will be negative, but since the question asks for “how many joules/calories are given off”, we report the
magnitude (positive value).
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Problem 1:
How many joules of heat are given off when 5.0 g of water cool from 75°C to 25°C?
*(Specific heat of water = 4.18 J/g°C)*
→ Temperature change:
ΔT = Final – Initial = 25°C – 75°C =
–50°C
(But since we’re calculating heat *given off*, we’ll use the absolute value for magnitude.)
Q = mass × |ΔT| × specific heat
Q = 5.0 g × 50°C × 4.18 J/g°C
Q = 5 × 50 × 4.18 =
1045 J
✔ Answer: 1045 J
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Problem 2:
How many calories are given off by the water in Problem 1?
*(Specific heat of water = 1.0 cal/g°C)*
Same mass and ΔT:
Q = 5.0 g × 50°C × 1.0 cal/g°C =
250 cal
✔ Answer: 250 cal
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Problem 3:
How many joules does it take to melt 35 g of ice at 0°C?
*(Heat of fusion = 333 J/g)*
Melting is a phase change → use Q = mass × heat of fusion
Q = 35 g × 333 J/g =
11655 J
✔ Answer: 11655 J
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Problem 4:
How many calories are given off when 85 g of steam condense to liquid water?
*(Heat of vaporization = 539.4 cal/g)*
Condensation is the reverse of vaporization → heat is *given off*
Q = mass × heat of vaporization
Q = 85 g × 539.4 cal/g =
45849 cal
✔ Answer: 45849 cal
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Problem 5:
How many joules of heat are necessary to raise the temperature of 25 g of water from 10°C to 60°C?
Temperature change:
ΔT = 60°C – 10°C =
50°C
Q = mass × ΔT × specific heat
Q = 25 g × 50°C × 4.18 J/g°C
Q = 25 × 50 × 4.18 =
5225 J
✔ Answer: 5225 J
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Problem 6:
How many calories are given off when 50 g of water at 0°C freezes?
*(Heat of fusion = 79.72 cal/g)*
Freezing is the reverse of melting → heat is *given off*
Q = mass × heat of fusion
Q = 50 g × 79.72 cal/g =
3986 cal
✔ Answer: 3986 cal
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✔ Final Answers:
1.
1045 J
2.
250 cal
3.
11655 J
4.
45849 cal
5.
5225 J
6.
3986 cal
Let me know if you’d like to see the calculations written out differently or with units shown more explicitly!
Parent Tip: Review the logic above to help your child master the concept of heat and its measurement worksheet answers.
