Thermal Properties of Matter Questions

Question 1
A circular hole of diameter 2.00 cm is made in an aluminium plate at 0 ⁰ C .what will be the diameter at 100⁰ C?
Linear expansion for aluminium = 2.3 * 10^-3 / ⁰ C

Solution:
Diameter of circular hole in aluminium plate at 0⁰ C=2.0 cm
With increase in temperature from 0⁰ C to 100⁰ C diameter of ring increases

using
L=L₀(1+αΔT)
where L0=2.0 cm
α = 2.3 * 10^-3 / ⁰ C
ΔT=(100 -0)=100 ⁰ C
we can find diameter at 100⁰ C
L=2(1+2.3*10^-3*100)
=2.46 cm

Question 2
The pressure of the gas in constant volume gas thermometer are 80 cm,90cm and 100cm of mercury at the ice point,the steam point and in a heated wax bath respectively.Find the temperature of the wax bath

Solution
Given that
Pressure at the ice point P_ice= 80 cm of Hg
Pressure at the steam point P_steam= 90 cm of Hg
Pressure at the wax bath P_wax= 100 cm of Hg
T=(P_wax-P_ice)X100/(P_steam-P_ice)
T = (100 - 80)X100/(90-80)
= 20X100/10
=200 ⁰C

Question 3
A rod of length L having coefficient of Linear expansion a is lying freely on the floor.it is heated so that temperature changes by b .Find the longitudinal strain developed in the rod
a. 0
b. ab
c. -ab
d. none of the above
Solution
There was no restriction for it expansion.So no tensile or compressive force developed.Longitudinal strains happens only when tensile or compressive force developed in the rod.So answer is a

Question 4
.if a is coefficient of Linear expansion,b coefficient of areal expansion,c coefficient of Volume expansion.Which of the following is true
a. b=2a
b. c=3a
c. b=3a
d. a=2b
Solution
Answer is c



Question 5
.which is of them is not used as the measurable properties in thermometer?
a.Resistance of platinum wire
b.Constant volume of gas
c.Constant pressure of gas
d.None of the above
Solution
Answer is d

Question 6
.when a solid metallic sphere is heated.the largest percentage increase occurs in its
a.Diameter
b. Surface area
c. Volume
d. density
Solution
Answer is c

Question 7
.the density of the liquid depends upon
a. Nature of the liquid
b. Temperature of the liquid
c. Volume of the liquid
d. Mass of the liquid
Solution
Answer is a and b
Question 8

A metallic sphere has a cavity of diameter D at its center.If the sphere is heated,the diameter of the . cavity will
a. Decrease
b. Increase
c. Remain unchanged
d. none of the above
Solution
Answer is b

Question 9
.A metallic circular disc having a circular hole at its center rotates about it axis passing through the center and perpendicular to it plane.when the disc is heated
a. Its speed will decrease
b. Diameter will increase
c. Moment of inertia will increase
d. its speed will increase
Solution
(a),(c)
Due to thermal expansion,the diameter of the disc as well of the hole will increase.therefore the moment of inertia will increase resulting in a increase in the angular speed.

Question 10
A resistance thermometer is such that resistance varies with temperature as
$R_T=R_0(1+aT+bT^5)$
where T represent Temperature on Celsius scale And a,b,R₀ are constants.R₀ unit is ohm
Based on above data ,Find out the unit of a,b
Solution
As per dimension analysis Unit on both sides should be equal
Now since R & R₀ both unit are same
Quantity $1+aT+bT^5$ should be dimension less
so at should be dimension less
so a unit is C^-1
similarly bT⁵ should be dimensionless
so b unit is C^-5


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