Where a = linear expansivity
L1 = original length before expansion
L2 = final length after expansion
∅1 = initial temperature before expansion
∅2 = final temperature after expansion
∆L = increase in length or change in length (L2 – L1)
∆∅ = temperature rise or change in temperature, (∅2 – ∅1)
The S.I unit of linear expansivity is per kelvin (k–¹)
Examples
- Steel bars, each of length 3m at 29⁰c are to be used for constructing a rail line. If the linear expansivity of steel is, 1.0 × 10–⁵k–¹, calculate the safety gap that must be left between successive bars if the highest temperature expected is 41⁰
c. WAEC 1989
Solution
The - A metal rod of length 50cm is heated from 40⁰C to 80⁰C. If the linear expansivity of the material is a, calculate the increase in length of the rod (in metres) in terms of a. WAEC 2008
- A metal rod of length 100cm, is heated through 100⁰C, calculate the change in length of the rod. ( Linear expansivity of the material of the rod is 3 × 10–⁵k–¹) WAEC 2003
- A bridge made of steel is 600m long. What is the daily variation in its length if the night-time and day-time temperature are 10⁰C and 35⁰C respectively. The linear expansivity of steel is 0.000012⁰C–¹
A. 0.18cm. B. 1.80cm. C. 18.0cm. D. 1800cm. JAMB 1992 - A metal rod of length 40.00cm at 20⁰C is heated to a temperature of 45⁰C. If the new length of the rod is 40.05cm, calculate its linear expansivity. WAEC 1994
- A brass rod is 2m long at a certain temperature. What is the length for a temperature rise of 100k, if the expansivity of brass is 18 × 10–⁶k–¹
A. 2.0036m. B. 2.0018m. C. 2.1800m. D. 2.0360m - The ratio of the coefficient of linear expansion of two metals a1/a2 is 3:4. If, when heated through the same temperature change, the ratio of increase in lengths of the two metals, e1/e2 is 1:2, the ratio of the original lengths L1/L2 is
A. ½. B. ⅜. C. ⁸/³. D. ⅔. Jamb 2007
AREA AND CUBIC EXPANSIVITIES
Area or superficial expansivity b of a substance is defined as the fractional increase in area of a piece of that substance per degree rise in temperature
Volume or cubic expansivity (y) of the substance is defined as the fractional increase in volume of a piece of that substance per degree rise in temperature.
Where A1 = original area or area at temperature ∅1
A2 = final area or area at temperature ∅2
V1 = original volume or volume at initial temperature ∅1
V2 = final volume or volume at initial temperature ∅2
∆A = change in area or increase in area (A2 – A1)
∆V = change in volume or increase in volume (V2 – V1)
Both area and volume expansivity are measured in (k–¹) - A solid metal cube of side 10cm, is heated from 10⁰c to 60⁰c. If the linear expansivity of the metal is 1.2 × 10–⁵k–¹, calculate the increase in its volume. WAEC 1993
- A piece of brass of mass 170kg has its temperature raised from 0⁰C to 30⁰C. Calculate its increase in volume, given the density of brass at 0⁰C as 8.5 × 10³kgm–³ and it’s cubic expansivity as 5.7 × 10–⁵k–¹. WAEC 1998
- The linear expansivity of brass is 2 × 10–⁵C–¹. If the volume of a piece of brass is 15.00cm³ at 0⁰C, what is the volume at 100⁰C? JAMB 1998
A. 16.03cm³. B. 16.00cm³. C. 15.09cm³. D. 15.03cm³ - A rectangular metal block of volume 10–⁶m³ at 273K is heated to 537K. If its coefficient of linear expansion is 1.2 × 10–⁵K–¹, the percentage change of its volume is? JAMB 1994
EXERCISE 2
2.. An iron rod of length 30cm is heated through 50 kelvin. Calculate its increase in length ⁰C [ Linear expansivity of iron = 1.2 × 10–⁵K–¹] WAEC 2000. ANS: 1.8×10–² - On a fairly cool rainy day when the temperature is 20⁰c, the length of a steel rail road track is 20m. What will be it’s length on a hot dry day when the temperature is 40⁰c?
A. 20.13m. B. 20.009m. C. 20.004m. D. 20.004m
[ Coefficient of linear expansion of steel = 11×10–⁶k–¹ ] JAMB 2003
Solution - A steel plug has a diameter of 5cm at 30⁰c. At what temperature will it fit exactly into a hole of constant diameter 4.997cm? [ Coefficient of linear expansion of steel is 11×10–⁶C–¹]
A. 27.3⁰c. B. -27.3⁰c. C. -2.7⁰C. D. 7.32⁰C. E. 2.7⁰c. JAMB 1978 - The ratio of the linear expansivity of copper to that of iron is approximately 1.5. A specimen of iron and a specimen of copper expand by the same amount per unit rise in temperature. The ratio of their length is____ A. 3. B. 1.5. C. 1.32. D. 1. E. 0.67. JAMB
- The linear expansivity of brass is 2 × 10–⁵ ⁰C–¹. If the volume of a piece of brass is 10cm³ at 0⁰C, what will be its volume at 100⁰C? A. 10.02cm³. B. 10.04cm³. C. 10.06cm³. D. 10.20cm³. D. 102.00cm³. JAMB 1987
- The length of a side of metallic cube at 20⁰c is 5.0cm. Give that the linear expansivity of the metal is 4.0×10–⁵k–¹, find the volume of the cube at 120⁰c. A. 126.50cm³. B. 126.25cm³. C. 126.00cm³. D. 125.00cm³. JAMB 1987
- A thin aluminium plate has a surface area of 1.500m² at 20⁰c. What will be it’s surface area when its cooler to -20⁰c? [ Take the linear expansivity of aluminum to be 2.5×10–⁵k–¹]
A. 1.503m³. B. 1.500m³. C. 1.498m³. D. 1.497m³. E. 1.490m³ - A blacksmith heated a metal whose cubic expansivity is 6.3 × 20–⁶k–¹. The area expansivity is____. A. 4.2×10–⁶k–¹. B. 2.0×10–⁶k–¹. . C. 6.3×10–⁶k–¹. D. 2.1×10–⁶k–¹.
