Cambridge International AS & A Level · 14 · structured

Specific heat and two kinds of latent heat

Specific heat and two kinds of latent heat · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand: demanding
Marks: 9
Topics: 2
Answer: Complete

structured9 marks

A 0.50 kg ice sample starts at −10.0 °C. Use c_ice=2100 J kg⁻¹ K⁻¹, L_f=3.34×10⁵ J kg⁻¹ and c_water=4200 J kg⁻¹ K⁻¹. Neglect heat loss. A separate vaporisation calculation uses L_v=2.26×10⁶ J kg⁻¹.

(a)
Define specific heat capacity, give its SI unit and find the energy to warm the ice to 0.0 °C.
3 marks
(b)
Define specific latent heat and distinguish fusion from vaporisation. Calculate the total energy to convert the original ice into water at 20.0 °C.
4 marks
(c)
Find the energy to vaporise a separate 0.020 kg of water already at its boiling temperature. State why Q=mcΔT is not the appropriate calculation for this stage.
2 marks

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Answer overview(a) Energy per kg per kelvin rise; J kg⁻¹ K⁻¹; 1.05×10⁴ J. (b) Energy per kg for a phase change at constant temperature; fusion solid→liquid, vaporisation liquid→gas; total 2.195×10⁵ J. (c) 4.52×10⁴ J; temperature is constant during the phase change.

(a)

3 marks

Define specific heat capacity, give its SI unit and find the energy to warm the ice to 0.0 °C.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

1
Specific heat capacity is energy required per unit mass per unit temperature rise without a change of phase.
2
Its unit is J kg⁻¹ K⁻¹.
3
Q=mcΔT=0.50×2100×10.0=10500 J.

(b)

4 marks

Define specific latent heat and distinguish fusion from vaporisation. Calculate the total energy to convert the original ice into water at 20.0 °C.

How to approach it

1
Latent heat per unit mass describes a phase-change energy transfer without a temperature change.
2
Fusion is solid to liquid; vaporisation is liquid to gas.
3
Melting requires mL_f=0.50×3.34×10⁵=167000 J.
4
Warming water needs 0.50×4200×20.0=42000 J; total=10500+167000+42000=219500 J.

(c)

2 marks

Find the energy to vaporise a separate 0.020 kg of water already at its boiling temperature. State why Q=mcΔT is not the appropriate calculation for this stage.

How to approach it

1
Q=mL_v=0.020×2.26×10⁶=45200 J.
2
The energy changes phase at constant temperature; using ΔT=0 in mcΔT would omit the latent energy.

Complete marking guidance

Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.

(a) Specific heat capacity is energy required per unit mass per unit temperature rise without a change of phase.
(a) Its unit is J kg⁻¹ K⁻¹.
(a) Q=mcΔT=0.50×2100×10.0=10500 J.
(b) Latent heat per unit mass describes a phase-change energy transfer without a temperature change.
(b) Fusion is solid to liquid; vaporisation is liquid to gas.
(b) Melting requires mL_f=0.50×3.34×10⁵=167000 J.
(b) Warming water needs 0.50×4200×20.0=42000 J; total=10500+167000+42000=219500 J.
(c) Q=mL_v=0.020×2.26×10⁶=45200 J.
(c) The energy changes phase at constant temperature; using ΔT=0 in mcΔT would omit the latent energy.

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