Class 10 Heat Exercise 9.1 Solutions | Science and Technology Curriculum Development Centre

Option D is the correct answer.

Cooling an object decreases its volume, whereas heating an object increases its volume.

To fit a wider pipe into a narrower pipe, we should make the dimensions of the wider pipe smaller. Similarly, we should increase the dimensions of the narrower pipe. We can achieve this by cooling the wider pipe and heating the narrower pipe.

Option B is the correct answer.

The lower fixed point of the thermometer is the temperature of the freezing point of ice.

In the Celsius scale, it is marked at $\rm 0^{o}C$. Similarly, in Fahrenheit and Kelvin scales, it is marked at $\rm 32^{o}F$ and $\rm 273 K$.

Thermal energy : The total kinetic energy of the particles within a substance.

• Example: The thermal energy of a pot of boiling water includes the energy from the movement of water molecules.

Heat : The transfer of thermal energy between systems or bodies due to a temperature difference.

• Example: When you touch a hot stove, heat flows from the stove (hot object) to your hand (cooler object).

The differences between Thermal energy and Heat are:

Following are the major differences between heat and temperature:

• Lower fixed point of a thermometer

The lower fixed point, also known as the ice point, is defined as the temperature at which pure water freezes (melting ice) at standard atmospheric pressure.

This point is marked at 0°C.

• Upper fixed point of a thermometer

The upper fixed point, referred to as the steam point, is defined as the temperature at which pure water boils (steam) at standard atmospheric pressure.

This point is marked at 100°C.

An iron bar is heated when hammered continuously for some time.

When the hammer strikes the iron bar, mechanical energy is transferred to the molecules of iron. This energy causes the molecules to vibrate more vigorously.

The impact increases the kinetic energy of the iron molecules. As they vibrate more, their average kinetic energy rises, leading to an increase in temperature.

Hence, iron bar is heated when it is hammered continuously.

When the tea in an open teacup reaches an equilibrium temperature with its surroundings, it stops cooling.

Heat flows from a body at a higher temperature to another body at a lower temperature. The net exchange of heat is zero when two bodies are at the same temperature.

In our case, when tea in an open teacup is hot (higher temperature), heat flows from it to its surroundings (lower temperature). This process continues until the temperature of the tea in the teacup matches the temperature of the surroundings. Thereafter, it does not lose its energy. Therefore, its temperature does not change. And, we observe that it has stopped cooling.

Hence, tea in an open teacup stops cooling after some time.

Water has a peculiar property of expansion known as anomalous expansion of water where it expands only after 4°C.

Hence, when water is cooled from 4°C to lower temperatures instead of contracting it expands. So, in cold places during winter such phenomenon takes place.

The expansion of water in lower temperature results in cracking of water pipes in cold places.

To cool the car's engine, water is kept in its radiator.

Water has a very high specific heat capacity (\(\rm 4200 Jkg^{-1}K^{-1} \)) compared to other liquids. Thus, it can absorb a large amount of heat from car's hot engine. It thus, prevents the engines from getting excessively hot.

A hot water bag is used to apply heat to parts of the body because water has a high specific heat capacity (\(\rm 4200 Jkg^{-1}K^{-1} \)) , meaning it can store and retain heat for a long time.

 When hot water is put into the bag, it slowly releases heat, which helps to soothe sore muscles, reduce stiffness, and improve blood circulation in the area. This gradual release of warmth provides consistent, gentle heat, making it effective for pain relief and relaxation.

In coastal areas, there is little temperature difference between day and night due to the high specific heat capacity of water, which is about 4,200 J/kg°C. This means water can absorb and store a large amount of heat without a rapid rise in temperature. 

During the day, the ocean absorbs heat from the sun, and at night, it slowly releases this stored heat. This gradual release warms the surrounding air, stabilizing temperatures and preventing extremes. 

Thus, the high specific heat capacity of water helps coastal areas maintain a mild climate with minimal temperature difference between day and night.

The night in a desert is very cold while the day is very hot.

It is because the specific heat capacity of sand is less; so its temperature changes fast. During days, the sand gets heated briskly and this results in a very hot day. 

At night, the sand gets cooled faster as it loses heat quickly due to its less specific heat capacity and causes a very cold night.

The perception that a bucket of lukewarm water contains more thermal energy than a large tank of cold water is a common misunderstanding.

Thermal energy refers to the total kinetic energy of all the particles in a substance. It depends on both the temperature of the substance and the number of particles present.

 On the other hand, temperature is a measure of the average kinetic energy of the particles in a substance. It indicates how hot or cold a substance is but does not directly indicate the total thermal energy.

A large tank of cold water contains significantly more water (and thus more particles) than a small bucket of lukewarm water. Even if the temperature of the lukewarm water is higher than that of the cold water, the sheer volume of cold water can result in greater total thermal energy.

Hence, the large tank, despite being colder, has many more particles contributing to its overall thermal energy.

When two bodies at different temperatures are placed in contact, heat flows from a body at higher temperature to a body at lower temperature until they reach to the same temperature which is called thermal equilibrium condition.

We a hot tea is touched the finger acts as a cold body and the hot tea cup acts as a hot body. The molecules of hot tea are vibrating with greater average kinetic energy than that of finger.

When in contact molecules of hot tea lose their energy to molecules of the finger until they vibrate with same average kinetic energy(temperature). In this way tea loses its heat to finger, hence on touching it feels hot.

Similarly, when touching an ice cube, there is loss and gain in kinetic energy of molecules of finger and ice until they reach the same average kinetic energy(temperature). In this case ice is cooler and the finger loses its heat to ice. 

Hence, the observer's finger is cooled on touching ice.

When the glass bottle with tight lid is heated, the lid of a glass bottle can be opened.

When you apply heat to an object, the temperature of that object increases, which in turn increases the kinetic energy of its molecules. The molecules begin to move more rapidly and vibrate more vigorously as they gain energy.

Different materials have different rate of expansion. So, due to difference in rate of expansion between lid and glass bottle, for same heat applied to them it may create a slight gap between the lid and the glass neck of the bottle.

In this way, the lid of the glass bottle could be opened.

Samir's experience of feeling the water warmer towards the bottom of a steel jug can be explained by the principles of heat transfer and the kinetic energy of molecules.

When Samir drinks from the steel jug, the water at the bottom of the jug is in direct contact with the surface that is likely warmer (e.g., a table or room temperature). Heat from this surface is conducted into the steel jug and subsequently into the water.

As heat is transferred to the water molecules at the bottom, their kinetic energy increases. This increase in kinetic energy causes the molecules to move faster, resulting in a higher temperature at the bottom compared to the top.

Hence, Samir felt the water to be warmer towards the bottom of the steel jug because of heat transfer from the jug to the water, which increases the kinetic energy of the molecules at the bottom.

The ice cube kept in the aluminum box will melt faster than the one in the wooden box.

When the two ice cubes of identical shape, one is kept in an aluminum box and the other in a wooden box, the thermal energy is transferred from aluminum and wooden box to ice cubes as the ice cubes are colder.

The aluminum box is a better heat conductor than the wooden box. Hence, the ice cube kept in an aluminum box will melt faster due to fast heat transfer from the aluminum box as compared to wooden box.

The specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of the unit mass of that substance through 1 Celsius degree (C$\rm ^{o}$).

Its SI unit is Joule/kg-Celsius (J/kg$\rm ^{o}C).

A mathematical relation that gives the relation between the quantity of heat lost or gained by a body (Q) with its mass (m), specific heat capacity (s), and change in temperature (d$\theta$) is called the heat equation which is as follows:

$$\rm Q = ms (d \theta )$$

Any two applications of specific heat capacity are as follows: 

1. Cooking: Water's high specific heat capacity helps cook food evenly because it takes a lot of heat to raise its temperature, preventing food from burning.
2. Weather: Large bodies of water, like oceans, help regulate temperatures in coastal areas. They absorb heat during the day and release it at night, influencing local weather patterns.

The boiling point of water at sea level at 1 atm pressure is 100^oC.

Pressure on liquids and their boiling points are directly proportional. It means that at higher atmospheric pressure boiling point is more and at low atmospheric pressure boiling point is less. 

This means that water can boil at lower temperatures when it is subjected to lower pressures. Practically, in mountainous regions, where atmospheric pressure is lower, water can boil at temperatures around 95°C or even lower.

The device which is used for measuring the temperature of a body is called a thermometer.

The types of thermometer used in our daily life and their working principles are:

1.Clinical Thermometer (Mercury and Alcohol)

Clinical thermometers, which include both mercury and alcohol as thermometric liquids, are designed specifically for measuring human body temperature.

Working principle of clinical thermometer:

This thermometer consists of a glass tube filled with thermometric liquid. As the body temperature increases, the liquid expands and rises in the tube. The level of liquid indicates the temperature on a calibrated scale.

2.Digital Thermometer

Working principle:

Digital thermometers use electronic sensors to measure temperature. When placed in contact with the body (oral, rectal, or underarm), the sensor detects the temperature and displays it numerically on a digital screen. They provide quick and accurate readings.

3. Infra-red Thermometer

Working principle:

The thermometer has a lens to focus infrared light from any object in front of its sensor called thermopile. The thermopile absorbs infrared radiation and turns it into heat. The more infrared energy, the hotter the thermopile gets. This heat is turned into electricity. The electricity is sent to a detector, which uses it to determine the temperature of any object it is pointed at.

The process of determining lower fixed point and upper fixed point on a newly constructed thermometer in order to make scale on it is called calibration of the thermometer.

Scale are to be made on a thermometer for its calibration. For making a scale, marking the lower fixed point and the upper fixed point is required. Hence, for calibrating a thermometer upper and lower fixed points are determined first.

Lower Fixed Point (Ice Point):

• Prepare a mixture of ice and water in a container.
• Insert the thermometer bulb into the ice-water mixture, ensuring it does not touch the sides or bottom of the container.
• Allow the thermometer to stabilize for several minutes until the thermometric liquid's level remains constant. Mark this level as lower fixed point.

Upper Fixed Point (Steam Point):

• Boil distilled water in a suitable container (like a flask) and ensure that steam surrounds the thermometer bulb.
• Insert the thermometer into the steam, ensuring it does not dip into the boiling water.
• After a few minutes, when the liquid level stabilizes, mark this level indicating the upper fixed point.

Calibration Scale:

• The distance between these two fixed points is divided into equal intervals, typically 100 equal divisions for Celsius  and Kelvin thermometers and 180 equal divisions for Fahrenheit thermometers.
• This division allows for accurate temperature readings between these two fixed points.

The required specific heat capacity of the substance is 126 J/kg-K.

Given,

mass (m) = 500 g = $\rm \frac{500}{1000} kg$ = 0.500 kg

initial temperature (T$\rm _{1}$) = 100$\rm ^{o}$C

final temperature (T$\rm _{2}$) = 226$\rm ^{o}$C

quantity of heat (Q) = 7938 J

To find: s = ?, where s is the specific heat capacity of the substance.

By using the formula for the quantity of heat, we get,

$\rm Q = ms \cdot \triangle T$

$\rm or, s = \frac{Q}{m \triangle T}$

$\rm or, s = \frac{Q}{m ( T_{2} - T_{1} )}$

$\rm or, s = \frac{7938}{0.500 \cdot (226 - 100)}$

$\rm \therefore s = 126 J/kg-K$