Thermal Expansion – Linear, Area, and Volume - UNSOLVED PRACTICE SET
Chapter: Thermal Properties of Matter | Topic: Thermal Expansion Linear Area Volume
THERMAL EXPANSION – LINEAR, AREA, AND VOLUME - UNSOLVED PRACTICE SET
Topic: Thermal Expansion Linear Area Volume
Multiple Choice Questions
Q1. The coefficient of linear expansion α is defined as:
- The increase in length per unit length per unit rise in temperature
- The increase in volume per unit volume per unit rise in temperature
- The increase in area per unit area per unit rise in temperature
- The total expansion of a body
Q2. The relationship between coefficients of linear (α), superficial (β), and cubical (γ) expansion is:
- α : β : γ = 1 : 2 : 3
- α : β : γ = 3 : 2 : 1
- α = β = γ
- α : β : γ = 1 : 3 : 2
Q3. A metal rod of length L is heated through ΔT. Its new length is:
- L(1 + αΔT)
- L(1 − αΔT)
- L/(1 + αΔT)
- LαΔT
Q4. When a metal plate with a hole in it is heated:
- The hole decreases in size
- The hole increases in size
- The hole remains the same size
- The hole changes shape
Q5. Water shows anomalous expansion:
- Between 0°C and 4°C
- Between 4°C and 100°C
- Above 100°C
- At all temperatures
Q6. A bimetallic strip bends on heating because:
- Both metals expand equally
- One metal expands more than the other
- Both metals contract
- One metal expands while the other contracts
Short Answer Questions
Q7. Define coefficient of linear expansion. Write its SI unit and dimensional formula.
Q8. A steel rod of length 2 m is heated from 20°C to 120°C. Calculate its expansion. (α for steel = 1.2 × 10⁻⁵ K⁻¹)
Q9. Explain why a small gap is left between railway tracks. What would happen if no gap were left?
Q10. In your school, a student observes that a metal lid on a glass jar loosens when heated. Explain this using thermal expansion.
Q11. A brass disc has a diameter of 10 cm at 20°C. Calculate its new diameter at 120°C. (α for brass = 2.0 × 10⁻⁵ K⁻¹)
Q12. Explain the anomalous expansion of water between 0°C and 4°C. Why is this important for aquatic life?
Long Answer Questions
Q13. Explain thermal expansion in solids, liquids, and gases. Derive the relationship between coefficients of linear, superficial, and cubical expansion (α, β, γ). Discuss the anomalous expansion of water and its biological significance. Why do different materials have different coefficients of expansion?
Q14. A steel tape measure is calibrated at 20°C. It is used to measure the length of a copper rod at 40°C. The reading is 50.00 cm.
(a) Calculate the actual length of the rod at 40°C, considering the expansion of the tape. (α_steel = 1.2 × 10⁻⁵ K⁻¹)
(b) Calculate the length of the rod at 20°C. (α_copper = 1.7 × 10⁻⁵ K⁻¹)
(c) What would the tape read if the measurement were made at 0°C?
(d) Discuss the importance of temperature correction in precision measurements.
(e) Why do surveyors measure at night or early morning?
Q15. Analyse the following engineering applications:
(i) Expansion joints in bridges
(ii) Bimetallic strips in thermostats
(iii) Glass containers for hot liquids
For each case, discuss:
(a) The principle of thermal expansion involved
(b) The design solution implemented
(c) What would happen if thermal expansion were ignored
Application-Based Problems
Q16. An aluminium rod (α = 2.4 × 10⁻⁵ K⁻¹) and a steel rod (α = 1.2 × 10⁻⁵ K⁻¹) have the same length of 2 m at 20°C.
(a) At what temperature will their lengths differ by 1 mm?
(b) If they are joined end-to-end to form a composite rod, calculate the total expansion when heated to 120°C.
(c) If they are joined side-by-side to form a bimetallic strip, calculate the radius of curvature at 120°C. (Thickness of each rod = 2 mm)
(d) Discuss why bimetallic strips are used in electrical thermostats.
(e) Calculate the thermal stress developed if the composite rod is constrained between rigid supports.
Q17. A glass flask of volume 500 cm³ is filled with mercury at 20°C. The flask is then heated to 80°C.
(a) Calculate the expansion of the flask. (γ_glass = 2.5 × 10⁻⁵ K⁻¹)
(b) Calculate the expansion of the mercury. (γ_mercury = 1.8 × 10⁻⁴ K⁻¹)
(c) Calculate the volume of mercury that overflows.
(d) Explain why mercury thermometers work on this principle.
(e) What would happen if water were used instead of mercury?
Q18. In a school experiment, students investigate the expansion of a metal rod using a spherometer and steam jacket.
(a) Describe the experimental setup and procedure.
(b) A rod of length 1 m shows an expansion of 1.2 mm when heated from 20°C to 100°C. Calculate α.
(c) If the rod is made into a pendulum, calculate the percentage change in time period when temperature rises by 50°C.
(d) Why does a pendulum clock run slow in summer?
(e) Suggest two methods to compensate for thermal expansion in precision pendulum clocks.