DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

JEE: DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

The document DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE is a part of the JEE Course DC Pandey Solutions for JEE Physics.
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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:
 DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
Putting TF = 0, we get TC = - 17.8°C
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

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

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:
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
∴ TC = 50°c
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
Now using the equation, DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
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:DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

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:
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
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: 
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
Temperature is decreased. Hence l or T will decrease. So it will gain time.
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
= 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
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
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: DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
Neglecting γ1γ2(DT)2 term, we get
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

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:

DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
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 .
∴  DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE ...(ii)
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
Substituting in Eq. (ii),
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
or DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE ...(iii)
Now we have an equation,
DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
From Eqs. (iii) and (iv), we get, γ= 1/T

The document DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE is a part of the JEE Course DC Pandey Solutions for JEE Physics.
All you need of JEE at this link: JEE

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