# Thermal Expansion - Long Question Answer | Physics Grade 11 Solution

### Long Question Solution

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Question: Describe a method to determine the linear expansivity of solid. Can the cubical expansivity be derived from this value?

Ans: The coefficient of linear expansion of given solid can be determined by using pullinger's apparatus. It consists of a rod of about 50cm in length whose coefficient of linear expansion is to be determined.  The rod is placed inside a metal tube called metal jacket which have inlet (I) for to enter through it and outlet (O) through steam can escape. The central hole of the tube is used to fix thermometer with the help of rubber cork. A spherometer is fixed on pillar 'P' with which we can measure the increase in length of rod. An electric circuit containing battery and galvanometer is connected between terminals T1 and T2. At first the length of the rod is measured as accurate as possible and it is placed inside the metal tube. The initial temperature of the rod is noted. The spherometer is turned forward till it touches end B of the rod and there is deflection in the galvanometer. The initial spherometer reading is noted. The spherometer is then turned backward to provide enough space for expansion. The steam is injected through inlet 'I'. After achieving the steady temperature the rod is heated for about 10 to 15 minutes. The final temperature of rod is noted. The spherometer again turned forward till it touches end B of the rod and there is deflection in the galvanometer the final spherometer reading is noted.

Let,
l1 = original length of the rod
θ1 = initial temperature of the rod
R1 = initial reading of spherometer
θ2 = final temperature of the rod
R2 = final reading of spherometer
α = coefficient of linear expansion
∆l = increase in length of the rod = R2 - R1

From the definition of α, we have
α = increase in length / (original length * rise in temperature)
= ∆l / l1∆θ
or, α = (R2 - R1) / l121)
On knowing the value of linear exapansivity of α the value of superficial expansivity and cubical expansivity can be determined by the experimental setup.

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