Study Guides/Physics/Thermal Capacities of Two Bodies in a Ratio — Concept and Problems
Study Guide · Physics

Thermal Capacities of Two Bodies in a Ratio

Thermal capacity (heat capacity) of a body is the amount of heat required to raise its temperature by 1°C (or 1 K). If the thermal capacities of two bodies are in ratio C₁:C₂ and equal heat is supplied, their temperature rises are in the inverse ratio C₂:C₁.

Question (Click to Flip)

What is thermal capacity?

Answer

Thermal capacity is the heat required to raise the temperature of a body by 1°C. C = mc (mass × specific heat). SI unit: J/K.

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Key Facts

Thermal capacity C = heat needed to raise the whole body by 1°C.

Formula: Q = C × ΔT.

Thermal capacity C = mass × specific heat = mc.

If C₁:C₂ = a:b, temperature rises ΔT₁:ΔT₂ = b:a (for same heat Q).

SI unit of thermal capacity: J/K.

Body with smaller C heats up more for the same heat input.

Thermal Capacity — Definition and Formula

Thermal capacity (C) = heat required to raise the temperature of a body by 1°C.

Formula: Q = C × ΔT

Where: • Q = heat supplied (in Joules or calories) • C = thermal capacity (in J/°C or cal/°C) • ΔT = rise in temperature

Relation to specific heat: C = m × c Where m = mass, c = specific heat capacity

SI unit of thermal capacity: J/K (joules per kelvin) or J/°C

Difference from specific heat: • Specific heat (c): property of the material; heat per unit mass per degree. • Thermal capacity (C): property of the body; depends on mass and material.

Ratio of Thermal Capacities — Temperature Rise

If thermal capacities of two bodies A and B are in ratio C₁:C₂:

For the same heat Q supplied to each: Q = C₁ × ΔT₁ = C₂ × ΔT₂

Therefore: ΔT₁/ΔT₂ = C₂/C₁

Conclusion: Temperature rises are in the INVERSE ratio of thermal capacities.

Example — ratio 3:4: C₁:C₂ = 3:4 → ΔT₁:ΔT₂ = 4:3 (Body with smaller thermal capacity heats up more for the same heat input.)

Example — ratio 1:2: C₁:C₂ = 1:2 ΔT₁:ΔT₂ = 2:1 Body A heats up twice as fast as body B for the same heat Q.

General rule: Smaller thermal capacity → greater temperature rise for the same heat.

Thermal Capacity vs Specific Heat Capacity

Property | Thermal Capacity | Specific Heat Definition | Heat for 1°C rise of the whole body | Heat for 1°C rise of unit mass Formula | C = mс | c = Q/(mΔT) Unit | J/K | J/(kg·K) Depends on | Mass and material | Material only Symbol | C (uppercase) | c (lowercase)

Specific heat values (common substances): • Water: 4200 J/(kg·K) — highest among common liquids • Aluminium: 900 J/(kg·K) • Copper: 385 J/(kg·K) • Iron: 450 J/(kg·K) • Lead: 128 J/(kg·K)

Practical example: 50 g copper (c=385) vs 50 g water (c=4200): C_copper = 0.05 × 385 = 19.25 J/K C_water = 0.05 × 4200 = 210 J/K Ratio = 19.25:210 ≈ 1:10.9 For same heat → water temperature rises ~10.9 times less.

Questions and Answers

What is thermal capacity?+

Thermal capacity is the heat required to raise the temperature of a body by 1°C. C = mc (mass × specific heat). SI unit: J/K.

If thermal capacities of two bodies are in ratio 3:4, what is the ratio of their temperature rises for equal heat?+

Temperature rises are in the inverse ratio: ΔT₁:ΔT₂ = 4:3. Since Q = CΔT, ΔT = Q/C, so smaller C gives greater ΔT.

What is the difference between thermal capacity and specific heat capacity?+

Thermal capacity (C = mc) depends on the mass and material of the whole body. Specific heat capacity (c) is a property of the material only — heat needed per unit mass per degree.

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