Sample QuestionsHeat and Temperature questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Consider the following statements.
$A.$ The coefficient of linear expansion has dimension $K^{-1}$.
$B.$ The coefficient of volume expansion has dimension $K^{-1}$.
Answer: A.
View full solution →A metal sheet with a circular hole is heated. The hole:
- ✓
- B
- C
Remains of the same size.
- D
Answer: A.
View full solution →Two identical rectangular strips, one of copper and the other of steel, are rivetted together to form a bimetallic strip $(\alpha_{\text{copper}}>\alpha_\text{steel})$. On heating, this strip will:
- A
- ✓
Bend with copper on convex side.
- C
Bend with steel on convex side.
- D
Answer: B.
View full solution →A system $X$ is neither in thermal equilibrium with $Y$ nor with $Z$. The systems $Y$ and $Z$:
- A
Must be in thermal equilibrium.
- B
Cannot be in thermal equilibrium.
- ✓
May be in thermal equilibrium.
- D
Answer: C.
View full solution →The temperature of water at the surface of a deep lake is $2^\circ C.$ The temperature expected at the bottom is:
- A
$0^\circ C$
- B
$2^\circ C$
- ✓
$4^\circ C$
- D
$6^\circ C$
Answer: C.
View full solution →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°C and a is the coefficient of linear expansion of the solid.
View full solution →A steel wire of cross-sectional area $0.5 \mathrm{~mm}^2$ is held between two fixed supports. If the wire is just taut at $20^{\circ} \mathrm{C}$, determine the tension when the temperature falls to $0^{\circ} \mathrm{C}$. Coefficient of linear expansion of steel is $1.2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ and its Young's modulus is $2.0 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$.
View full solution →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.
A tightly closed metal lid of a glass bottle can be opened more easily if it is put in hot water for some time. Explain.
A steel ball initially at a pressure of $1.0 \times 10^5 \mathrm{~Pa}$ is heated from $20^{\circ} \mathrm{C}$ to $120^{\circ} \mathrm{C}$ keeping its volume constant. Find the pressure inside the ball. Coefficient of linear expansion of steel $=12 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}$ and bulk modulus of steel $=1.6 \times$ $10^{11} \mathrm{Nm}^{-2}$.
View full solution →In a Callender's compensated constant pressure air thermometer, the volume of the bulb is 1800 cc. When the bulb is kept immersed in a vessel, 200 cc of mercury has to be poured out. Calculate the temperature of the vessel.
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 →The density of water at $0^{\circ} \mathrm{C}$ is $0.998 \mathrm{~g} \mathrm{~cm}^{-3}$ and at $4^{\circ} \mathrm{C}$ is $1000 \mathrm{~g} \mathrm{~cm}^{-3}$. Calculate the average coefficient of volume expansion of water in the temperature range 0 to $4^{\circ} \mathrm{C}$.
View full solution →If mercury and glass had equal coefficient of volume expansion, could we make a mercury thermometer in a glass tube?
A concrete slab has a length of 10 m on a winter night when the temperature is $0^{\circ} \mathrm{C}$. Find the length of the slab on a summer day when the temperature is $35^{\circ} \mathrm{C}$. The coefficient of linear expansion of concrete is $1.0 \times 10^{-5^{\circ}} \mathrm{C}^{-1}$.
View full solution →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 →A circular hole of diameter $2.00 cm$ is made in an aluminium plate at $0^{\circ} \mathrm{C}$. What will be the diameter at $100^{\circ} \mathrm{C}$ ? $\alpha$ for aluminium $=2.3 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$.
View full solution →A metre scale made of steel reads accurately at $20^\circ C$. In a sensitive experiment, distances accurate up to $0.055mm$ in $1m$ are required. Find the range of temperature in which the experiment can be performed with this metre scale. Coefficient of linear expansion of steel = $11 \times {10}^{-6}{^\circ C}^{-1}$.
View full solution →An aluminium can of cylindrical shape contains $500cm^3$ of water. The area of the inner cross section of the can is $125cm^2$. All measurements refer to $10^\circ C$. Find the rise in the water level if the temperature increases to $80^\circ C$. The coefficient of linear expansion of aluminium = $23 \times {10^{-6}} { ^\circ C}^{-1}$ and the average coefficient of volume expansion of water = $3.2 \times {10^{-4}} { ^\circ C}^{-1}$ respectively.
View full solution →Two metre scales, one of steel and the other of aluminium, agree at $20^{\circ} \mathrm{C}$. Calculate the ratio aluminium-centimetre/ steel-centimetre at:
a. $0^{\circ} \mathrm{C}$,
b. $40^{\circ} \mathrm{C}$
c. $100 \mathrm{C} . \alpha$ for steel $=1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}{ }^{-1}$ and for aluminium $=2.3 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$.
View full solution →A metre scale is made up of steel and measures correct length at $16^{\circ} \mathrm{C}$. What will be the percentage error if this scale is used:
a. On a summer day when the temperature is $46^{\circ} \mathrm{C}$.
b. On a winter day when the temperature is $6^{\circ} \mathrm{C}$ ? Coefficient of linear expansion of steel $=11 \times 10^{-60} \mathrm{C}^{-1}$.
View full solution →Can the bulb of a thermometer be made of an adiabatic wall?
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.
Why do marine animals live deep inside a lake when the surface of the lake freezes?