📐 Chapter 10: Thermal Physics – Numerical Problems
Prepared by Muhammad Tayyab, Subject Specialist Physics, Govt Christian High School Daska. Based on PECTAA 2026 syllabus (National Curriculum 2023).
📖 What's Inside: This section covers numerical problems from the official PECTAA 2026 curriculum: volume expansion of water, linear expansion of steel rod, temperature change from expansion, specific heat capacity of iron, latent heat of fusion (ice melting), and latent heat of vaporization (water boiling). Each problem includes step-by-step solutions with formulas.
📚 Related Resources – Chapter 10: Thermal Physics
Practice numerical problems to master thermal physics calculations for board exams.
📑 Quick Jump to Problems
📖 Numerical Problems & Solutions (PECTAA 2026)
10.2 Volume Expansion of Water
A container holds 1 litre of water at 20°C. What will be its volume at 80°C? (β = 2.1 × 10⁻⁴ per °C)
📊 Given Data:
V₀ = 1 litre = 1000 cm³, T₀ = 20°C, T = 80°C, ΔT = 60°C, β = 2.1 × 10⁻⁴ °C⁻¹
V₀ = 1 litre = 1000 cm³, T₀ = 20°C, T = 80°C, ΔT = 60°C, β = 2.1 × 10⁻⁴ °C⁻¹
\[ V = V_0 (1 + \beta \Delta T) \]
\[ V = 1000 [1 + (2.1 \times 10^{-4})(60)] \]
\[ V = 1000 [1 + 0.0126] = 1000 \times 1.0126 = 1012.6 \text{ cm}^3 \]
✅ Answer: 1012.6 cm³
10.3 Linear Expansion of Steel Rod
A steel rod initially measures 2m at 20°C. If α = 1.2 × 10⁻⁵ °C⁻¹, what will be its length at 100°C?
📊 Given Data:
L₀ = 2 m, T₀ = 20°C, T = 100°C, ΔT = 80°C, α = 1.2 × 10⁻⁵ °C⁻¹
L₀ = 2 m, T₀ = 20°C, T = 100°C, ΔT = 80°C, α = 1.2 × 10⁻⁵ °C⁻¹
\[ L = L_0 (1 + \alpha \Delta T) \]
\[ L = 2 [1 + (1.2 \times 10^{-5})(80)] \]
\[ L = 2 [1 + 9.6 \times 10^{-4}] = 2 \times 1.00096 = 2.00192 \text{ m} \]
✅ Answer: 2.00192 m
10.4 Temperature Change from Expansion
A steel bridge expands by 5 cm on a hot summer day. If the bridge originally spanned 100 m, what is the temperature change? (α = 1.2 × 10⁻⁵ °C⁻¹)
📊 Given Data:
L₀ = 100 m, ΔL = 5 cm = 0.05 m, α = 1.2 × 10⁻⁵ °C⁻¹
L₀ = 100 m, ΔL = 5 cm = 0.05 m, α = 1.2 × 10⁻⁵ °C⁻¹
\[ \Delta L = \alpha L_0 \Delta T \implies \Delta T = \frac{\Delta L}{\alpha L_0} \]
\[ \Delta T = \frac{0.05}{(1.2 \times 10^{-5})(100)} = \frac{0.05}{1.2 \times 10^{-3}} = 41.67°C \]
✅ Answer: 41.67°C
10.5 Specific Heat Capacity of Iron
How much heat is required to raise the temperature of a 2 kg iron bar from 20°C to 100°C? (c = 450 J kg⁻¹ K⁻¹)
📊 Given Data:
m = 2 kg, T₀ = 20°C (293 K), T = 100°C (373 K), ΔT = 80 K, c = 450 J kg⁻¹ K⁻¹
m = 2 kg, T₀ = 20°C (293 K), T = 100°C (373 K), ΔT = 80 K, c = 450 J kg⁻¹ K⁻¹
\[ Q = m c \Delta T \]
\[ Q = (450)(2)(80) = 72000 \text{ J} = 72 \text{ kJ} \]
✅ Answer: 72 kJ
10.6 Latent Heat of Fusion (Ice Melting)
How much heat is required to melt 500 g of ice at 0°C into water at 0°C? (Lf = 3.36 × 10⁵ J kg⁻¹)
📊 Given Data:
m = 500 g = 0.5 kg, Lf = 3.36 × 10⁵ J kg⁻¹
m = 500 g = 0.5 kg, Lf = 3.36 × 10⁵ J kg⁻¹
\[ Q = m L_f \]
\[ Q = (0.5)(3.36 \times 10^5) = 168000 \text{ J} = 168 \text{ kJ} \]
✅ Answer: 168 kJ
10.7 Latent Heat of Vaporization
Calculate the heat required to completely vaporize 1 kg of water at 100°C. (Lv = 2.26 × 10⁶ J kg⁻¹)
📊 Given Data:
m = 1 kg, Lv = 2.26 × 10⁶ J kg⁻¹
m = 1 kg, Lv = 2.26 × 10⁶ J kg⁻¹
\[ Q = m L_v \]
\[ Q = (1)(2.26 \times 10^6) = 2.26 \times 10^6 \text{ J} = 2.26 \text{ MJ} \]
✅ Answer: 2.26 MJ
10.1 Coefficient of Linear Expansion
A metal rod of length 1.5 m expands by 0.025 m when heated from 30°C to 180°C. Calculate its coefficient of linear expansion.
📊 Given Data:
L₀ = 1.5 m, ΔL = 0.025 m, T₀ = 30°C, T = 180°C, ΔT = 150°C
L₀ = 1.5 m, ΔL = 0.025 m, T₀ = 30°C, T = 180°C, ΔT = 150°C
\[ \alpha = \frac{\Delta L}{L_0 \Delta T} \]
\[ \alpha = \frac{0.025}{(1.5)(150)} = \frac{0.025}{225} = 1.11 \times 10^{-4} \text{ K}^{-1} \]
✅ Answer: 1.11 × 10⁻⁴ K⁻¹
10.2 Latent Heat of Fusion
How much heat is required to melt 600 g of ice at 0°C into water at 0°C? (Lf = 3.36 × 10⁵ J kg⁻¹)
📊 Given Data:
m = 600 g = 0.6 kg, Lf = 3.36 × 10⁵ J kg⁻¹
m = 600 g = 0.6 kg, Lf = 3.36 × 10⁵ J kg⁻¹
\[ Q = m L_f \]
\[ Q = (0.6)(3.36 \times 10^5) = 201600 \text{ J} = 201.6 \text{ kJ} \]
✅ Answer: 201.6 kJ
📐 Key Formulas – Thermal Physics
Linear Expansion: \( \Delta L = \alpha L_0 \Delta T \) or \( L = L_0(1 + \alpha \Delta T) \)
Volume Expansion: \( \Delta V = \beta V_0 \Delta T \) or \( V = V_0(1 + \beta \Delta T) \)
Heat Transfer: \( Q = mc\Delta T \)
Latent Heat of Fusion: \( Q = m L_f \)
Latent Heat of Vaporization: \( Q = m L_v \)
💡 Exam Tip:
For numerical problems in board exams, always follow these steps: 1) Write given data with proper units, 2) Identify the relevant formula, 3) Substitute values carefully, 4) Show calculation steps, 5) Write final answer with correct units. These numerical problems follow the PECTAA 2026 pattern and are prepared by Subject Specialist Muhammad Tayyab.
Unit 10✨ Thermal Physics
Unit 11Transfer of Thermal Energy
Unit 12Waves
Unit 13Sound
Unit 14Light
Unit 15Electrostatics
Unit 16Electricity
Unit 17Electromagnetism
Unit 18Electromagnetic Induction & EM Waves
Unit 19Electronics
Unit 20Atomic and Nuclear Physics
Unit 21Space and Environment
📖 Complete syllabus coverage for Class 10 Physics (PECTAA 2026) – Units 10 to 21
Created by Hira Science Academy | Aligned with PECTAA 2026 Syllabus