Linear expansivity is defined as the increase in length, of the unit length of the material for one degree temperature rise.

In order to solve any question on linear expansity:

(i) Write down the formula

(ii) Write down the data given

(iii) Understand what you are asked to find

(iv) Make proper substitution

(v) Evaluate

Question 1

A wire of length 100.0m at 300C has a linear expansivity of 2 x 10-5K-1. Calculate the length of the wire at a temperature of -100C{UTME 2013}

A. 99.92m B. 100.08m C. 100.04m D. 99.96m

Solution

l1 = new length

l0 = original length

Q = temperature change

0.00002 = change in length / 100(30-(-10))

0.00002 = change in length / 100*40

0.00002*4000 = change in length

change in length = 0.08

change in length = 100 – x

x = 100 – 0.08 = 99.92m

A is the correct option

Question 2

Two metals P and Q are heated through the same temperature difference. If the ratio of the linear expansivities of P to Q is 2: 3 and the ratio of their lengths is 3:4 respectively, the ratio of the increase in lengths of P to Q is{UTME 2012}

A. 1 : 2 B. 2 : 1 C. 8 : 9 D. 9 : 8

Solution

Temperature difference =( linear expansivity * length)/increase in length

For metal P,

Qp = ( linear expansivity * length)p/increase in lengthp

For metal Q,

Qq = ( linear expansivity * lengthq)/increase in lengthq

( linear expansivity * length)p/increase in lengthp = ( linear expansivity * lengthq)/increase in lengthq

increase in length of p:increase lengthq = ( linear expansivity * length)p / ( linear expansivity * lengthq)

increase in length of p:increase lengthq = 2/3 *3 /4 = 6 / 12 = 1:2

A is the correct option

Question 3

A metal of volume 40cm3 is heated from 300C to 900C, the increase in volume is{UTME 2011}

A. 0.40cm3 B. 0.14cm3 C 4.00cm3 D. 1.20cm3.

[Linear expansivity of the metal= 2.0 x 10-5K-1]

Solution

cubic expansivity = 3* linear expansivity = 3 * 0.00002 = 0.00006

0.00006 = increase in volume / 40*(90 – 30)

0.00006 = increase in volume / 40*60

increase in volume = 0.00006*2400 = 0.144cm3

B is the correct answer

Question 4

A blacksmith heated a metal whose cubic expansivity is 6.3 x 10-6K-1. The area expansivity is{UTME 2007}

A. 6.3 x 10-6K-1 B. 4.2 x 10-6K-1 C. 2.1 x 10-6K-1 D. 2.0 x 10-6K-1

Solution

cubic expansivity = 3* linear expansivity

0.0000063 = 3*linear expansivity

linear expansivity = 0.0000063/3 = 0.0000021

Area expansivity = 2*0.0000021 = 0.0000042

B is the correct option

Question 5

Calculate the length which corresponds to a temperature of 20^0C if the ice and steam points of an ungraduated

thermometer are 400 mm apart

A. 80mm

B. 20mm

C. 30mm

D. 60mm

Solution

ice point = lower fixed point = 0^oC

steam point = upper fixed point = 100^oC

(100 -0)/(20 -0) = 400/(x – 0)

100/20 = 400 / x

20*400 = 100x

x = 8000/100

x = 80mm

A is the correct option

Question 6

A steel bridge is built in the summer when its temperature is 35.0°C. At the time of construction, its length is 80.00m. What is the length of the bridge on a cold winter day when its temperature is -12.0°C? (Linear expansivity of steel is 1.2 x10^-5)

Solution

initial length = 80 m

initial temperature = 35.0°C

final length = ?

final temperature = -12.0°C

Change in temperature = final – initial = -12-35 = -47.0°C

let change in length = x

o.oooo12 = x/80(-47)

x = 0.000012*80*(-47) = -0.04512 m

note

x = final length – initial length

-0.04512 = final length – 80

final length = 80 -0.04512 = 79.95488 m

The length of the bridge on a cold winter day = 79.95488 m