Multiple choice questions on thermal properties of matter
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Multiple Choice questions
Question 1:
There are three Rods A,B,C of equal length L at same temperature .There coefficient of linear expansion are αa, αb, αr respectively. if the temperature of all rod are increased by θ ° C and coefficient of linear expansion is like αb>αa >αc. then what will be the final order of length of rod
a. Lc>Lb>Lc
b. Lb= La= Lc
c. La>Lb>Lc
d. Lb>La>Lc
Answer
L = L0 (1 + αθ)
if L0 & θ are same
then
L is directly proportional to α
So answer will be
Lb > La > Lc
Question-2:
Three bodies are having temperature
TA = - 42 °F
TB = - 10 °C
TC = 2000 K
Which body among these is most warm
a, TA
b, TB
c, TC
d, None of these
Answer
Let us calculate all body temperature on same scale
Let choose Celsius
C = K - 273.15
C=(5F-160)/9
TA= - 42 °F = (5 x -42 - 160 )/ 9
= -41 °C
TB = - 10 °C
TC= 200 K = 200 - 273
= - 73.1 °C
So most warm body is TB
Question-3
A sphere of mass m and diameter D is Heated by temperature ΔT , if Coefficient of linear expansion is α what will be the change in the Surface Area
a, π D2α ΔT (α ΔT+ 2)
b. π D2α ΔT (α ΔT- 2)
c. π D2α ΔT (α ΔT+ 4)
d. π D2α ΔT (α Δ- 4)
Answer
Initial Surface Area = 4πR2
= 4 π (D/2)2
= 4 π D2 / 4 = π D2
Surface Area at ΔT
= 4π(D'/2)2
Now
D'=D(1+α ΔT)
So Surface Area at ΔT
= 4π(D2/4 )(1+α ΔT)2
= π D2 (1+ α2ΔT2 + 2α ΔT)
Change in surface Area
= π D2 (α2ΔT2 + 2α ΔT)
= π D2α ΔT (α ΔT+ 2)
Question-4
if α is the Coefficient of linear expansion of block and L denotes length, T denotes Temperature then which one of these is true
a, dL - α L dT = 0
b, dL + α L dT = 0
c, αdL - L dT = 0
D, αdL - +L dT = 0
Answer
From the definition of linear expansion
α= (1/L)(dL/dT)
αL dT = dL
dL - αL dT = 0
So a is correct
Question-5
Consider the following statement
A.If body A and body B are in state of thermal equilibrium, B & C are in state of thermal equilibrium then A & C are in Equilibrium
B. If body A and body B are not in equilibrium and A & C are not in thermal equilibrium then B & C may be in thermal equilibrium.
a. Only A is Correct
b. Only b is Correct
c. A & B is Correct
d. Neither is correct
Question-6
For any material, density ρ , mass m and volume V are related by ρ = m/V and B is coefficient of volume expansion then which one is true
a, B = (1/ρ) (dρ/ dT)
b, B = -(1/ρ) (dρ/ dT)
C, B = (1/ρ) (dρ/ dV)
d, B = (1/ρ) (dρ/ dV)
Answer
ρ = m/V
ρV = m
differentiating at w.r.t T
d(ρV)/dT = 0
ρ(dV/dT) = - V(dρ/dT)
dV/VdT= - (1 /ρ) (dρ/ dT)
Now since B =dV/VdT
So B = -(1/ρ) (dρ/ dT)
Question-7
A constant volume air thermometer works on
a, Pascal law
b, Charles law
c, Boyles law
d, Archimedes
Answer
Ans. Charles, Law
Question-8
10 litres of benzene weight
a, more in summer than in winter
b, more in winter than in Summer
c, equal in winter and summer
d, none of above
Answer
Density decrease with increase in temp. So same volume will weigh less with increase in temperature
since summer are hotter than winter
so winter will have more weight
Question-9
An Aluminium Rod of length L0rest on a smooth horizontal base if the temperature is increase by ΔT °C. What will be the longitudinal strain developed
a, αΔT
B, Zero
c. -αΔT
D. none of the above
Answer
Zero Since no tensile stress is there, so strain will be zero
Question-10
A metal ball immersed in alcohol weight m1 at 0 °C and m2 at 150 °C. The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that density of metal is large as compared to that alcohol ,it can be shown
a. m1- m2>0
b. m1- m2<0
c. m1=m2
d none of the above
Answer
Let αm and αa are cubical expansion of metal and alcohol
V be the volume of metal at 0 °C
and Ma weight of metal in air
Given αm < αa
m1 = Ma - Vρag
m2 = mass in air - Vρag [(1+αm150)/1+αa150)]
Now 1+αm150 < 1+αa150
as αm < αa
so m2 = mass in air - Vρag(Something less than one)
So that means m2 > m1
Question-11
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
Answer
it is known by formula
b=2a
c=3a
Question-12
the coefficient of linear expansion of an in homogeneous rod changes linearly from α1to α2from one end to the other end of the rod. The effective coefficient of linear expansion of the rod is
a. α1+α2
b. 1/2(α1+α2)
c. √α1α2
d. None of the these
Answer
Consider a small element of length dx from one end of the rod. Let L be the length of the rod. Now the increase in the coefficient of linear expansion by unit length of the rod is (α2-α1)/L. Therefore the value of α of the element located at x is
αx=α1 +x(α2-α1)/L.
Therefore increase in length of the element is αxdxΔT where ΔT is the rise in temperature.Therefore the increase in the length of the rod is
L=∫αxdxΔT
integrating between the limits 0 and L = 1/2(α1+α2)LΔT
Question 13
Which of the following devices is used to detect thermal radiation?
a. Thermopile
b. Constant volume air thermometer
c. Liquid thermometer
d. Six Maximum and minimum thermometer
Answer
Answer is a
Question 14 The sprinkling of water reduces the temperature of the closed room
a. The water has large latent heat of vaporization
b. Water is bad conductor of heat
c. Specific heat of water is high
d. the temperature of water is less than that of room
Answer
Sprinkled water vaporises by taking the heat from the room.The latent heat of vaporization is very high so it takes large heat to vaporize and room becomes cool
So a is correct
Question 15
As the temperature is increased, the time period of a pendulum
(a) increases as its effective length increases even though its centre of mass still remains at the centre of the bob.
(b) decreases as its effective length increases even though its centre of mass still remains at the centre of the bob.
(c) increases as its effective length increases due to shifting of centre of mass below the centre of the bob.
(d) decreases as its effective length remains same but the centre of mass shifts above the centre of the bob
