Heat
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Chapter – 3
Heat
Exercise
5. Solve the mathematical problems:
(a)
Soln,
mass (m) = 500g = 500/1000 = 0.5kg
T1 = 15°C
T2 = 85°C
specific heat capacity = 4200 J
we k it,
Q = msdt
= 0.5 × 4200 × (85 − 15)
= 2100 × 70
= 147000 J
= 147000 / 1000
= 147 kJ.
(b)
[The question statement is not written on this page in the supplied source.]
Solution for (b)
specific heat capacity (s) = 460 J/kg
T1 = 43°C
T2 = 30°C
mass = 5kg
Q = ?
we k it,
Q = msdt
= 5 × 460 × (43 − 30)
= 2300 × 13
= 29900 J.
(c)
1st condition:
mass = 2kg
Q = 4200 J
dt = 10°C
s = ?
Q = msdt
s = Q / mdt
= 4200 / (2 × 10)
= 4200 / 20
= 210 J/kg°C.
2nd condition:
mass = 4kg
Q = ?
s = 210
T1 = 20°C
T2 = 40°C
Now,
we k it,
Q = msdt
= 4 × 210 × (40 − 20)
= 840 × 20
= 16800 J.
(d)
Solution for (d)
mass = 500g = 0.5kg.
Q = 7938 J
t1 = 100°C
t2 = 226°C
specific heat capacity (s) = ?
Now,
Q = msdt
s = Q / mdt
= 7938 / [0.5 × (226 − 100)]
= 7938 / (0.5 × 126)
= 7938 / 63
= 126 J/kg°C.
(e)
soln,
for cold water:
mass = 16kg
t1 = 25°C
t2 = x
heat gain = msdt
= 16 × s (x − 25) — (i)
for hot water:
mass = 4kg
t1 = 80°C
t2 = x
heat loss = msdt
= 4 × s (80 − x) — (ii)
for heat equation,
heat gain = heat loss
16s(x − 25) = 4s(80 − x)
4(x − 25) = 80 − x
4x − 100 = 80 − x
5x = 180
∴ x = 36°C.
2. Differentiate between:
(a) Thermal energy and Heat
| Thermal energy | Heat |
|---|---|
| The average kinetic energy between the molecules of a substance is called thermal energy. | Heat is a form of energy which gives us sensation of warmth. |
| It is a form of energy. | It is a form of energy transfer. |
(b) Heat and Temperature
| Heat | Temperature |
|---|---|
| Heat is a form of energy which gives us sensation of warmth. | The degree of hotness or coldness of a body is called temperature. |
| It’s SI unit is Joule (J). | It’s SI unit is Kelvin (K). |
(c) Lower fixed point and Upper fixed point
| Lower fixed point | Upper fixed point |
|---|---|
| The temperature at which pure ice melts in normal pressure is called lower fixed point. | The temperature at which pure water boils in normal pressure is called upper fixed point. |
| It’s value is 0°C. | It’s value is 100°C. |
3. Give reason:
(a) An iron box heats when it is hammered continuously for some time.
→ Because while hammering, the tiny molecules of the iron box vibrate very highly which leads to the energy up of the heat.
(b) Tea in an open tea cup stops cooling after some time.
→ Because tea loses heat to the surrounding which is colder than the tea and loses until it reaches the same temperature.
(c) Water pipes crack in cold places in the winter.
→ Water pipes crack in cold places in the winter due to the anomalous expansion of water in which water expands due to which the pressure inside the pipe increases when freezing.
(d) To cool the car’s engine water is kept in its radiator.
→ Because a body of radiator absorbs a large amount of heat and cannot increase its temperature due to its high specific heat capacity.
(e) The hot water bag is used to give heat pressure to the painful body.
→ Because the high specific heat capacity of hot water keeps the heat for a long time and release it slowly.
(f) There is no significant difference in temperature between the day time and the night time in coastal area.
→ Because coastal area are influenced by the thermal properties between the daytime and the nighttime in coastal areas.
(g) Temperature differs a lot between the day and night in the desert.
→ Because the soil/sand desert have low specific heat capacity which heats in day time very rapidly, getting heat, and at night time loses rapidly.
4. Answer question:
(a) In the perception of certain man, a bucket of lukewarm water contains more thermal energy than a large tank of chilled water. Comment this understanding based on the definition of thermal energy and temperature.
→ According to the heat eqn.
From heat equation, thermal energy refers to the total kinetic energy of particles in a substance, while temperature is the degree of
hotness or coldness of a body. A large tank of cold water might indeed have more total thermal energy than a lukewarm water because the thermal energy is directly proportional with the temperature and quantity of the substance.
(b) Touching a cup of hot tea feels hot but touching an ice cube feels cool. Explain it based on the motion of their molecules.
→ Touching a cup of hot tea feels hot because the rapid motion of their molecules transfers energy to our skin which makes us feel hot. In case of ice cube, the slow moving molecules transfer less energy to our skin, making it feel cold.
(c) If the lid of a glass bottle does not open, how may it be opened using your knowledge based on the effects of heat? Explain based on the kinetic energy of molecules.
→ If the lid of a glass bottle doesn’t open, I will hot the lid of the bottle which will increase the kinetic
energy produced between molecules resulting in the expansion of the lid.
(d) Study the relationship between the volume and temperature of water shown in the given graph and answer the following questions:
(i) What is the special property of water shown in the graph called?
→ The special property of water shown in the graph is called anomalous expansion of water.
(ii) Mention the change in volume of water that happens when water is heated from 0°C to 4°C.
→ The volume of water decreases up to 4°C and after 4°C the volume of water increases.
(iii) How does the property of water shown in the graph differ from the property of other liquids?
→ The property of water shown in graph is different because in other liquid volume increase from 0°C but water decrease up to 4°C then increase.
(iv) Explain the importance of this knowledge in daily life.
[No answer is written below this question in the supplied source.]
(v) Draw a model graph to show the relationship between the density of water and temperature based on the relationship shown by graph.
(e) [Question wording partly unclear in the supplied source.]
→ In winter the cold air is more dense near the floor while warm air rises. Similarly in the [Unreadable in source], the colder air near the surface of the water descends towards the bottom, displacing the warmer water upward. The result, when water in the bottom slightly feel warmer. It can be justified on the principle of convection.
(f) What are the differences between the process of freezing water and honey in terms of their volume and density?
→ When we freeze water after 4°C and decreasing volume, this is because its cooling causes into hexagonal solid. It has a lower density resulting to a decrement of volume.
When we freeze honey it expands and increase in volume. This expansion occurs due to the formation of ice crystals with the honey which takes up more
space than liquid honey.
In terms of density, ice generally has a higher density than a liquid phase while the honey has a lower density compared to liquid honey.
(g) Of the two boxes of identical shape, one is kept in an aluminium box and the other in a wooden box. Which ice cube melts faster? Explain in terms of the melting process.
→ The ice cube kept in the aluminium box will melt faster than the ice on a wooden box. In this is because aluminium is a good conductor of heat while wood is a poor conductor. The aluminium box allows heat from the surrounding to transfer more efficiently to the ice cube, increasing the rate of heat transfer and melting. In contrast, the wooden box acts as an insulator, reducing the heat transfer to the ice cube, thus slowing down the melting process.
(h) What is specific heat capacity? Write its SI unit.
→ The heat required to change the temperature of a substance of 1kg mass by 1°C is the specific heat capacity of that substance. Its SI unit is Joule per kilogram per degree Celsius (J/kg°C).
(i) What is the heat equation?
→ The equation which shows relation between amount of heat gained or lost by a body is called heat equation.
According to this equation, heat gained or lost by a body is equals to (Q) heat × mass × specific heat × temperature becomes equal.
(j) Write any two applications of specific heat capacity.
→ Two applications of specific heat capacity:
- Water bandage is used to relief from high fever.
- Hot water bag is used to relief from back pain.
(k) Describe the condition which water can be boiled at temperature less than 100°C.
→ Water can be boiled at a temperature less than 100°C when the surrounding atmospheric pressure is reduced. As the atmospheric pressure decreases, this phenomenon is observed at high altitude where the atmospheric pressure is lower than at sea level. At higher altitudes water can boil at temperatures below 100°C because the reduced atmospheric pressure allows water molecules to escape the liquid phase and vaporize more easily.
(l) Write the types of thermometers used in daily life. Also mention their working principles.
→ IN NOTE.
(m) What is thermometer calibration? Describe.
→ Thermometer calibration is the process of determining the scale of a thermometer. For calibration a thermometer, the temperature of melting ice (0°C) is taken as lower fixed point and the temperature (100°C) of the steam just above the surface of pure water boiling at one atmospheric pressure is taken as the upper fixed point.
Notes
Heat
Heat is a form of energy which gives the sensation of warmness. It is produced by the vibration of molecules.
In normal conditions heat always transfer from hot to cold body. Its SI unit is Joule and CGS unit is calorie. i.e. 1 calorie = 4.2 Joule. It is measured by calorimeter.
Temperature
The degree of hotness and coldness of a body is called temperature. It is measured by using instrument called thermometer. Temperature is measured in 4 scales:
- Celsius scale: The scale having lower fixed point as 0°C and upper fixed point as 100°C is called Celsius scale.
- Fahrenheit scale: The scale having lower fixed point as 32°F and upper fixed point as 212°F is called Fahrenheit scale.
- Kelvin scale: The scale having lower fixed point as 273K and upper fixed point as 373K is called Kelvin scale.
- Reaumur scale: The scale having lower fixed point as 0°R and upper fixed point as 80°R is called Reaumur scale.
The SI unit of temperature is Kelvin (K).
Transformation formula for different scale
Absolute zero temperature
The temperature at which every kinetic energy of molecules become 0 is called absolute zero temperature. Its value is 0K or −273.15°C.
Effects of heat on volume
Heat is directly proportional to volume of a substance i.e. when heat increases volume increase and vice versa.
A substance gets sufficient energy for their motion and volume increases.
Normal expansion
Every substance expands on heating but water shows different property that is when water is heated from 0°C to 4°C its volume decreases and from 4°C above its volume increases (density decreases). This different property shown by water is called anomalous expansion of water.
Effects of anomalous expansion of water
- Pipes burst in winter season in higher region.
- Aquatic animals are alive in frozen pond.
Heat equation
The equation which gives relation between amount of heat gained or lost by a body is called heat equation.
According to this equation, heat gained by cold body is equal to heat lost by hot body until their temperature becomes equal.
According to heat equation amount of heat gained or lost is:
1stly, directly proportional to mass of body.
2ndly, directly proportional to change in temperature.
Combining eqn (i) and (ii):
Q ∝ m(t2 − t1)
Q = ms(t2 − t1)
Q = msdt
Where s is proportionality constant called specific heat capacity.
Specific heat capacity
We have,
Q = msdt
s = Q / mdt
when,
m = 1kg
dt = 1°C
Then s = Q.
Definition
The total amount of heat required to rise the temperature of unit mass of the substance by 1°C is called specific heat capacity. Its SI unit is J/kg°C and CGS unit is cal/g°C.
The specific heat capacity depends upon 3 factors:
- Q ∝ s (Q = amount of heat)
- s ∝ 1/m (m = mass of the substance)
- s ∝ 1/dt (dt = change in temperature)
The specific heat capacity of water is 4200 J/kg°C in SI unit and 1 cal/g°C in CGS unit.
The specific heat capacity of water is 4200 J/kg°C. It means 4200 Joule of heat energy is required to rise the temperature of 1kg of water by 1°C.
Applications of high value of specific heat capacity of water
- Water bandage is used to relief from high fever.
- Water is used to cool the engines of vehicles.
- Hot water bags is used to relief from back pain.
Thermometer
An instrument which is used to measure the temperature of a substance is called thermometer.
Types of Thermometer
- Liquid thermometer: The thermometer in which liquid is used as thermometric substance is called liquid thermometer. It works on the expansion of volume of liquid on heating. There are 2 types of liquid thermometer.
- Mercury thermometer: The thermometer in which mercury is used as thermometric substance is called mercury thermometer. Its melting point is −39°C and boiling point is 357°C. So it is used to measure temperature of hot regions.
- Alcohol thermometer: The thermometer in which alcohol is used as thermometric substance is called alcohol thermometer. Its melting point is −115°C and boiling point is 78°C. So it is used to measure temperature of cold regions.
- Radiation Thermometer: The thermometer which is used to measure temperature of a body without physical contact by using different radiations is called Radiation Thermometer.
- Digital Thermometer: The thermometer in which heat sensitive sensor called thermistor is used as a working substance is called digital thermometer.
- Gas Thermometer: The thermometer in which gas is used as thermometric substance is called gas thermometer. It works on the principle of expansion of gas on heating.
Calibration of Thermometer
The process of giving proper scaling in a thermometer is called calibration of thermometer. During calibration there are 2 fixed points in a thermometer.
- Upper fixed point (UFP): The temperature at which pure water boils is called upper fixed point.
- Lower fixed point (LFP): The temperature at which pure ice melts is called lower fixed point.
Discussion
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