Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev

DC Pandey (Questions & Solutions) of Physics: NEET

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NEET : Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev

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Introductory Exercise 17.1

Ques 1: What is the value of
(a) 0°F in celsius scale?
(b) 0 K on Fahrenheit scale?
Sol:
 Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Putting TF = 0, we get TC = - 17.8°C
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev

Ques 2: At what temperature is the Fahrenheit scale reading equal to (a) twice (b) half of Celsius?
Sol: 
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Putting TF = 2Twe get TC = 160° C
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev

Ques 3: A Fault y thermometer reads 5°C in melting ice and 99°C in steam. Find the correct temperature in °F when this faulty thermometer reads 52°C.
Sol:
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
∴ TC = 50°c
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Now using the equation, Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Putting TC = 50° C, we get TF = 122°F

Ques 4: At what temperature the Fahrenheit and Kelvin scales of temperature give the same reading?
Sol:Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev

Putting TF = TK,
We get, TF or TK = 574.25

Ques 5: At what temperature the Fahrenheit and Celsius scales of temperature give the same reading?
Sol:
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Putting TC =TF, we get
TC or TF =-40°C or -40°F

Ques 6: A pendulum clock of time period 2 sec gives the correct time at 30°C. The pendulum is made of iron. How many seconds will it lose or gain per day when the temperature falls to 0°C?
αFe = 1.2 × 10-5 (°C)-1.
Sol: 
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Temperature is decreased. Hence l or T will decrease. So it will gain time.
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
= 15.55 s

Ques 7: A block of wood is floating in water at 0°C. The temperature of water is slowly raised from 0°C to 10°C. How will the percentage of volume of block above water level change with rise in temperature?
Sol: 
Density of water will increase by increasing the temperature from 0 to 4°C, then it will decrease. Fraction of volume immersed is given by
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
ρ1 is first increased the decreased first decreased the increased.
Or percentage of volume above water level will first increased then decreased.

Ques 8: A piece of metal floats on mercury. The coefficient of volume expansion of metal and mercury are γ1 and γ2 respectively. If the temperature of both mercury and metal are increased by an amount ΔT, by what factor does the fraction of the volume of the metal submerged in mercury changes?
Sol: Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev

Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Neglecting γ1γ2(DT)2 term, we get
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev

Ques 9: A brass disc fit s snugly in a hole in a steel plate. Should you heat or cool the system to loosen the disc from the hole? Given that αB > aFe.
Sol:

Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Since, αB >αFe
On cooling brass will contract more.

Ques 10:Show that the volume thermal expansion coefficient for an ideal gas at constant pressure is 1/T.
Sol: 
PV = nRT ...(i)
At constant pressure we can write the above equation as
PdV = nRdT .
∴  Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev ...(ii)
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
Substituting in Eq. (ii),
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
or Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev ...(iii)
Now we have an equation,
Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 1) - Physics, Solution by DC Pandey NEET Notes | EduRev
From Eqs. (iii) and (iv), we get, γ= 1/T

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