Show that moment of inertia of a solid body of any shape changes with temperature as $\text{I}=\text{I}_0(1+2\alpha\theta),$ where $\text{I}_0$ is the moment of inertia at $0^\circ C$ and a is the coefficient of linear expansion of the solid.
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Heat and Temperature question types
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48
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1 Marks Question
2 Q→022 Marks Questions
17 Q→033 Marks Question
12 Q→044 Marks Questions
2 Q→055 Marks Questions
15 Q→Sample Questions
Heat and Temperature questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
A steel wire of cross$-$sectional area $0.5\ mm^2$ is held between two fixed supports. If the wire is just taut at $20^\circ C,$ determine the tension when the temperature falls to $0^\circ C.$ Coefficient of linear expansion of steel is is $1.2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ and its Young's modulus is $2.0 \times 10^{11}N m^{-2}.$
View full solution →A steel rod is clamped at its two ends and rests on a fixed horizontal base. The rod is unstrained at $20^\circ C.$ Find the longitudinal strain developed in the rod if the temperature rises to $50^\circ C.$ Coefficient of linear expansion of steel $=1.2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}.$
View full solution →A spherical shell is heated. The volume change according to the equation $\text{V}_\theta=\text{V}_\theta(1+\gamma\theta)$. Does the volume refer to the volume enclosed by the shell or the volume of the material making up the shell?
View full solution →A steel rod of length $1m$ rests on a smooth horizontal base. If it is heated from $0^\circ C$ to $100^\circ C,$ what is the longitudinal strain developed?
View full solution →If two bodies are in thermal equilibrium in one frame, will they be in thermal equilibrium in all frames?
A gas thermometer measures the temperature from the variation of pressure of a sample of gas. If the pressure measured at the melting point of lead is 2.20 times the pressure measured at the triple point of water, find the melting point of lead.
If mercury and glass had equal coefficient of volume expansion, could we make a mercury thermometer in a glass tube?
The density of water at $0^\circ C$ is $0.998g \ cm^{-3}$ and at $4^\circ C$ is $1000g \ cm^{-3}.$Calculate the average coefficient of volume expansion of water in the temperature range $0$ to $4^\circ C.$
View full solution →Is it possible for two bodies to be in thermal equilibrium if they are not in contact?
Find the ratio of the lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature. Coefficients of linear expansion of iron and aluminium are $12 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}$ and $23 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}$ respectively.
View full solution →Does the temperature of a body depend on the frame from which it is observed?
Why do marine animals live deep inside a lake when the surface of the lake freezes?
If an automobile engine is overheated, it is cooled by putting water on it. It is advised that the water should be put slowly with engine running. Explain the reason.
Two metre scales, one of steel and the other of aluminium, agree at $20^\circ C$. Calculate the ratio aluminium$-$centimetre/ steel$-$centimetre at:
View full solution →- $0^\circ C,$
- $40^\circ C$
- $100C. \alpha for steel = 1.1 \times 10^{-5 }^\circ C^{-1}$ and for aluminium$= 2.3 \times 10^{-5} ^\circ C^{-1}.$
A metre scale is made up of steel and measures correct length at $16^\circ C$. What will be the percentage error if this scale is used:
View full solution →- On a summer day when the temperature is $46^\circ C$.
- On a winter day when the temperature is $6^\circ C$? Coefficient of linear expansion of steel $= 11 \times 10^{-6^\circ} C^{-1}.$
An aluminium plate fixed in a horizontal position has a hole of diameter $2.000\ cm$. A steel sphere of diameter $2.005\ cm$ rests on this hole. All the lengths refer to a temperature of $10^\circ C$. The temperature of the entire system is slowly increased. At what temperature willl the ball fall down? Coefficient of linear expansion of aluminium is $23 \times 10^{-6^\circ} C^{-1 }$ and that of steel is $11 \times 10^{-6^\circ} C^{-1}$.
View full solution →Two steel rods and an aluminium rod of equal length $l_0$ and equal cross section are joined rigidly at their ends as shown in the figure below. All the rods are in a state of zero tension at $0^\circ C$. Find the length of the system when the temperature is raised to $\theta$. Coefficient of linear expanaion of aluminium and steel are $\alpha_\text{a}$ and $\alpha_\text{s}$respectively. Young's modulus of aluminium is $Y_a$ and of steel is $Y_s.$
View full solution →A glass vessel measures exactly $10\ cm \times 10\ cm \times 10\ cm$ at $0^\circ C$. It is filled completely with mercury at this temperature. When the temperature is raised to $10^\circ C, 1.6\ cm^3$ of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass $= 6.5 \times 10^{-6 ^\circ} C.$
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