Chapter 4 – Thermal phenomena | Chapter Solution Class 10

The linear expansion of a solid is the increase in its length per unit length per degree rise in temperature.

The types of expansion in solid are:

1. Linear expansion,
2. Areal expansion or superficial expansion, and
3. Volume expansion.

Rubber.

The coefficient of linear expansion of a solid is the increase in its length per unit length per degree rise of temperature.

per degree Celsius (°C⁻¹) or per Kelvin (K⁻¹).

No, liquids do not have a definite shape, so the concept of linear expansion is not applicable to them.

It means that for every 1°C rise in temperature, the length of brass increases by 1.8 × 10⁻⁵ times its original length.

α=β/2=γ/3

No, it depends only on temperature and is expressed in °C⁻¹ or K⁻¹.

No, liquids do not have a definite shape and expand in volume rather than length, so linear expansion is not possible for liquids.

Liquids are always contained in a vessel. When heated, both the liquid and the container expand, but the expansion of the container is not noticeable. The observed expansion of the liquid is called apparent expansion.

Gases do not have a fixed shape or volume and expand freely in all directions. The expansion of the container is negligible compared to the expansion of the gas, so there is no apparent expansion in gases.

Thermal conduction is the transfer of heat through a substance without the movement of its particles, due to temperature differences within the substance.

Aluminium and copper.

Wood and glass.

Watt per meter per Kelvin (W m⁻¹ K⁻¹)

Steel rails expand in summer due to thermal expansion. If there are no gaps, the rails may bend and cause derailments. To allow for expansion and contraction, gaps are left between the rails.

The outer surface of the chimney cools rapidly, while the inner surface remains hot and expands. This uneven expansion causes internal stress, leading to cracking of the glass.

A bimetallic strip is made of two different metals joined together. When heated, the strip bends, as one metal expands more than the other. This proves that different metals expand at different rates.

Experiment: Cubic expansion of an iron ball on heating

Take an iron ball and a ring such that the ball just passes through the ring as shown in fig (a). Now, heat the ball and try to pass it through the ring. You will find that the ball does not pass through the ring fig (b). Why is this so?

When the ball is heated, it expands and its size increases. After some time, when the ball coos, it will again pass through the ring. This experiment shows that solids expand on heating and contract on cooling.

Coefficient of linear expansion: The coefficient of linear expansion of a solid is the increase in its length per unit length per degree rise of temperature.

The mathematical expression of the coefficient of linear expansion:

α=l_2−l_1\over l_1(t_2−t_1)

l₁ = Initial length

l₂ = Final length

t₁ = Initial Temperature

t₂ = Final Temperature

Unit of the coefficient of linear expansion:

It is expressed as per degree Celcius (^oC^-1) or per degree kelvin (K^-1)

Aim: To show that liquid expands on heating

Things Required: An empty bottle, cork having a hole drilled, a drinking straw, wire gauze, tripod stand, burner

Procedure: Take a bottle fill it completely with water and add drops of ink to it to make it coloured.

Fix the cork in the mouth of the bottle and pass the drinking straw through the cork. Put some molten wax around the hole to avoid the leakage of water.

Pour some more water into the drinking straw so that the water level in the straw can be seen.

There are two types of expansion of a liquid because when a liquid contained in a solid container is heated, the solid container undergoes expansion along with the liquid.

1. Take an empty bottle. The empty bottle contains air.
2. Attach a rubber balloon to its neck as shown in figure.
3. The balloon is deflated initially.
4. Place the bottle above the burner. It heats the air present in bottle.
5. After sometime it is noticed that the balloon gets inflated as shown in figure.

Conclusion — This shows that on heating, air present inside bottle expands and fills the balloon. So the balloon gets inflated. This shows that air expands on heating.

Charle’s law: At constant pressure, the volume of a given mass of a gas increases or decreases by 1/273 of its volume at 0°C for each one-degree rise or fall in temperature.

The mathematical form of Charle’s law:

V_t=V_o(1+t/273)

V_o = volume at 0°C

V_t = volume at t°C

Experiment

Take a rod or flat strip of metal. Fix a few small wax pieces on the rod. These pieces should be at nearly equal distances. Clam the rod to a stand or place one end of the rod in between two bricks. Heat the other end of the rod with a candle.

Observation

The heat from the candle side passes towards the other end by dissolving wax pieces on the rod.

Conclusion

This experiment shows that heat is transferred from the hotter end to the colder end.

There is no material movement of the rod.

Good conductors are those substances through which heat is easily conducted

Example: iron, copper

Bad conductors are those substances through which heat is not conducted easily

Example: wood, cloth

Ball and Ring Experiment : This well known experiment shows that the solids expand on heating and contract on cooling. The apparatus consists of a metallic ball and ring such that at room temperature the ball just passes through the ring [Fig]. On placing the ball after heating, on the ring, we find that the ball is not passing through the ring i. e., the ball has been increased in volume on heating. When the ball is left for some time we find that on cooling, it passes again through the ring. i. e., there is contraction of the ball on decreasing the temperature.

Charles’ Law states that, at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature.

The reason why pressure is kept constant in Charles’ Law is that the volume of a gas is highly dependent on the pressure it is subjected to. If the pressure were to change while the temperature remained constant, the volume would also change, making it difficult to establish a direct relationship between the two.

Charle’s law: At constant pressure, the volume of a given mass of a gas increases or decreases by 1/273 of its volume at 0°C for each one-degree rise or fall in temperature.

The mathematical form of Charle’s law:

V_t=V_o(1+t/273)

V_o = volume at 0°C

V_t = volume at t°C

Pressure is kept constant in Charles’ law to isolate the effect of temperature on the volume of a gas, ensuring changes in volume are directly proportional to changes in temperature.

Good conductors are materials that allow heat or electricity to flow through them easily. Examples of good conductors include metals such as copper, aluminium, gold, and silver.

Bad conductors, also known as insulators, are materials that do not allow heat or electricity to flow through them easily. Examples of bad conductors include rubber, wood, plastic, and air.

The coefficient of thermal expansion is defined as the fractional increase in length or volume per unit rise in temperature.

The SI unit of the coefficient of thermal expansion is 1/K.

1. Thermal
2. length
3. reciprocal
4. given
5. Mercury

1. False
2. True
3. True
4. False
5. True

1. (c)
2. (d)
3. (b)
4. (e)
5. (a)

(d) γ/3

Explanation:

The coefficient of linear expansion (α) is related to surface expansion (β) and volume expansion (γ) by β = 2α and γ = 3α. Rearranging gives α = γ/3, meaning linear expansion is one-third of volume expansion. Hence, the correct answer is γ/3.

(c) trapped air

Explanation:

Metals like copper and iron are good conductors because they allow heat to pass easily. Trapped air, however, is a poor conductor as air molecules are far apart, reducing heat transfer. This is why trapped air is used for insulation in thermos flasks, winter clothing, and double-glass windows, making it the correct answer.

(a) uneven expansions

Explanation:

A bimetallic strip is made of two metals with different thermal expansion rates. When heated, one metal expands more, causing the strip to bend toward the metal with less expansion. This principle is used in thermostats and temperature switches, confirming that uneven expansion is the correct answer.