Heat and Temperature
OBJECTIVE - I
2. Which of the curves in figure(23-Q1) represents the relation between Celsius and Fahrenheit temperatures?
OBJECTIVE - I
1. A system X is neither in thermal equilibrium with Y nor with Z. System Y and Z
(a) must be in thermal equilibrium
(b) cannot be in thermal equilibrium
(c) maybe in thermal equilibrium.
Answer: (c).
Explanation: Suppose X is at a temperature A and Y and Z are both at temperature B, in such a case the given condition may happen. Hence the option (c).
2. Which of the curves in figure(23-Q1) represents the relation between Celsius and Fahrenheit temperatures?
The figure for Q-2
Answer: (a).
Explanation: The relation between Celsius and Fahrenheit is given by:-
F = (9/5)C + 32
In other terms it is
C =(5/9)F -160/9
It is in the form of y=mx+c, which is an equation of a straight line. Here the gradient m = 5/9. Since it is less than 1, the line makes an angle less than 45°. Also, the intercept on the C-axis is -160/9. So the line 'a' represents this relationship. So the option (a) is correct.
F = (9/5)C + 32
In other terms it is
C =(5/9)F -160/9
It is in the form of y=mx+c, which is an equation of a straight line. Here the gradient m = 5/9. Since it is less than 1, the line makes an angle less than 45°. Also, the intercept on the C-axis is -160/9. So the line 'a' represents this relationship. So the option (a) is correct.
3. Which of the following pairs may give equal numerical values of the temperature of a body?
(a) Fahrenheit and Kelvin
(b) Celcius and Kelvin
(c) Kelvin and Platinum.
Answer: (a).
Explanation: The relation between Fahrenheit and Kelvin is
F = 9/5(K-273.16)+32
Putting F = K, we get
5F = 9F-9*273.16 +160 =9F-2298.44
→4F =2298.44
→F = 574.61
So at this temperature, both Kelvin and Fahrenheit will read the same temperature. Hence the option (a).
There is always a difference of 273.16 between the Celsius and Kelvin scale, hence there will be no temperature the same for both the scale. Hence the option (b) is wrong.
Platinum is not a scale like Kelvin but a medium through which temperature can be measured in other scales. Hence the option (c) is wrong.
4. For a constant volume gas thermometer, one should fill the gas at
(a) low temperature and low pressure
(b) low temperature and high pressure
(c) high temperature and low pressure
(d) high temperature and high pressure.
Answer: (c).
Explanation: In a constant volume thermometer, the temperature depends upon the mass of the gas in the bulb. This difference reduces to a great extent if the mass of the gas is very less. This can be achieved with high temperature and low pressure. Hence the option (c).
5. Consider the following statements.
(A) The coefficient of linear expansion has dimension K⁻¹.
(B) The coefficient of volume expansion has dimension K⁻¹.
(a) A and B are both correct.
(b) A is correct but B is wrong.
(c) B is correct but A is wrong.
(d) A and B are both wrong.
Answer: (a).
Explanation: The coefficient of linear expansion α =(ΔL/L)/T and the coefficient of volume expansion
Ɣ = (ΔV/V)/T.
In both the cases, ΔL/L and ΔV/V are dimensionless and the temperature T is in the denominator. Hence both will have dimensions of K⁻¹. The option (a) is correct.
6. A metal sheet with a circular hole is heated. The hole
(a) gets larger
(b) gets smaller
(c) remains of the same size
(d) gets deformed.
Answer: (a).
Explanation: The hole in the metal sheet behaves like the same metal in expansion because the metal expands in the outer direction. You can also assume the hole-size metal sheet at that place. When heated this piece will also expand. So the hole at that place will also expand. Option (a) is correct.
7. Two identical rectangular stripes, one of copper and the other of steel, are riveted together to form a bimetallic strip(αcopper >αsteel). On heating, this strip will
(a) remain straight
(b) bend with copper on the convex side
(c) bend with steel on the convex side
(d) get twisted.
Answer: (b).
Explanation: The coefficient of linear expansion of copper is more than steel, so for the same temperature difference copper strip will expand more than the steel strip. Hence the copper strip will be on the convex side. Option (b).
8. If the temperature of a uniform rod is slightly increased by 𐊅t, its moment of inertia 'I' about perpendicular bisector increases by
(a) zero
(b) αI𐊅t
(c) 2αI𐊅t
(d) 3αI𐊅t.
Answer: (c).
Explanation: M.I. of a uniform rod about its perpendicular bisector is,
I = ML²/12.
Length after temperature increase
L' =L(1+αΔt)
→L'-L = LαΔt
Now, M.I.
I' = ML'²/12
The change in M.I. = I' - I
=(L'²-L²)M/12
=(L'+L)(L'-L)M/12
=L(2+αΔt)*LαΔt*M/12
=2L²αΔt*M/12, {Neglecting small term Δt²}
=2αΔt*(ML²/12)
=2αIΔt.
Hence the option (c).
I = ML²/12.
Length after temperature increase
L' =L(1+αΔt)
→L'-L = LαΔt
Now, M.I.
I' = ML'²/12
The change in M.I. = I' - I
=(L'²-L²)M/12
=(L'+L)(L'-L)M/12
=L(2+αΔt)*LαΔt*M/12
=2L²αΔt*M/12, {Neglecting small term Δt²}
=2αΔt*(ML²/12)
=2αIΔt.
Hence the option (c).
9. If the temperature of a uniform rod is slightly increased by 𐊅t, its moment of inertia 'I' about a line parallel to itself will increase by
(a) zero
(b) αI𐊅t
(c) 2αI𐊅t
(d) 3αI𐊅t.
Answer: (a).
Explanation: Though the length of the rod will increase, all the mass will remain at the same distance from the axis. Since M.I. = ∫r²dm, it will remain unchanged. Hence the option (a).
10. The temperature of water at the surface of a deep lake is 2°C. The temperature expected at the bottom is
(a) 0°C
(b) 2°C
(c) 4°C
(d) 6°C.
Answer: (c).
Explanation: Since the density of water is maximum at 4 °C, it will be heavier and remain at the bottom. Hence the option (c).
11. An aluminum sphere is dipped into water at 10°C. If the temperature is increased, the force of buoyancy
(a) will increase
(b) will decrease
(c) will remain constant
(d) may increase or decrease depending on the radius of the sphere.
Answer: (b).
Explanation: When the temperature is increased further, the aluminum sphere also expands. It displaces more volume of water. The force of buoyancy is the weight of the water displaced. Though the volume of water is more its weight is less than the previously displaced water because its density is reduced. Density is reduced because of the coefficient of volume expansion of water is about 10 times more than the aluminum. So the force of buoyancy reduces. Hence the option (b).
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CHAPTER- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
CHAPTER- 14 - Fluid Mechanics
CHAPTER- 13 - Fluid Mechanics
CHAPTER- 12 - Simple Harmonic Motion
CHAPTER- 11 - Gravitation
CHAPTER- 10 - Rotational Mechanics
CHAPTER- 9 - Center of Mass, Linear Momentum, Collision
CHAPTER- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
CHAPTER- 14 - Fluid Mechanics
CHAPTER- 13 - Fluid Mechanics
CHAPTER- 12 - Simple Harmonic Motion
CHAPTER- 11 - Gravitation
CHAPTER- 10 - Rotational Mechanics
CHAPTER- 9 - Center of Mass, Linear Momentum, Collision
CHAPTER- 8 - Work and Energy
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CHAPTER- 7 - Circular Motion
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CHAPTER- 6 - Friction
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CHAPTER- 6 - Friction
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CHAPTER- 5 - Newton's Laws of Motion
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CHAPTER- 4 - The Forces
The Forces-
"Questions for short Answers"
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CHAPTER- 3 - Kinematics - Rest and Motion
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CHAPTER- 2 - "Physics and Mathematics"
CHAPTER- 2 - "Physics and Mathematics"
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