1. What is anomalous expansion of water?
Ans: The property of water in which water contracts on heating from 0oC to 4oC and then expands on further heating from 4oC is called anomalous expansion of water.
2. Why does water overflow from the beaker when the beaker full of water at 4oC is heated?
Ans: This is because water at 4oC has minimum volume and when the beaker full of water at 4oC is heated, water expands for which it overflows from the beaker.
3. If a 2kW electric immersion heater is used to warm 200 kg of water at 200C, calculate
a. The quantity of heat energy given out by immersion of heat in 2 hours’ time
b. Final temperature of water.
(Ans: 1440000J and 37.14°C)
4. On what factors does the quantity of heat of an object depend? How much heat is required to raise the temperature of 500 gm. of water from 5°C to 30°C?
Ans: We have the heat equation,
where,
m = Mass of body
Q = Heat energy of a body
s = Specific heat capacity of body
dt = change in temperature
Hence, quantity of heat energy of an object depends in following factors:
• Mass of object
• Specific heat capacity of object
• Change in temperature
Here,
Given,
For water,
Mass (m) = 500 gm. = 0.5 kg
Initial temperature (t1) = 5°C
Final temperature (t2) = 30°C
Specific heat capacity (s) = 4200 J/kg°C
Heat energy (Q) =?
According to the heat equation,
Q =msdt
where,
m = Mass of body
Q = Heat gained or lost by a body
s = Specific heat capacity of the body
dt = Change in temperature
Q = 0.5 х 4200 х (30 — 5) = 52,500 J
Hence, the heat energy required to raise the temperature of 500 gm. water from 5°C to 25°C is 5.25х104 J.
5. What do you mean by the statement that the specific heat capacity of water is 1 Cal/gmoC?
Ans: The statement means that 1 gm of water requires 1 Calorie heat energy to raise its temperature by 1oC.
6. What do you mean by the statement that the specific heat capacity of iron is iron is 470 J/kgoC?
7. Why is water used in hot water bag?
Ans: Water is used in hot water bag because water has high specific heat capacity and water in hot water bag remains hot for a longer time than any other liquid.
8. Calculate the final temperature when 2400 J of heat is given to an iron of mass 2 kg at 200C. (siron = 460 Jkg-1 °C-1)
9. What is temperature?
According to the molecular theory, temperature is the average kinetic energy of the molecules of a body.
10. What is absolute zero?
11. On which factor does the temperature of a body depend?
12. A metal ball of mass 200 gram at 83°C is plunged into 300 gram of water at 30°C. If the final temperature of the mixture is 33°C, calculate the specific heat capacity of metal.
Given,
Final temperature of mixture (t) = 33°C
For metal ball,
Mass (m1) = 200 gm. = 0.2 kg
Initial temperature (t1) = 83°C
Specific heat capacity (s1) =?
For water,
Mass (m2) = 300 gm. = 0.3 kg
Initial temperature (t2) = 30°C
Specific heat capacity (s2) = 4200 J/kg°C
According to heat equation,
Q = msdt
where,
m = Mass of body
Q = Heat gained or lost
s = Specific heat capacity of body
dt = Change in temperature
Again,
According to principle of calorimetry, the amount of heat gained is equal to the amount of heat lost.
So,
Heat lost by metal ball = Heat gained by water
m1s1dt1 = m2s2dt2
Or, 0.2 х s1 х (83 — 33) = 0.3 х 4200 х (33 — 30)
s1 = 378 J/kg°C
Hence, the specific heat capacity of metal 378 J/kg°C.
13. Three liquids A, B, C of equal mass are kept in the same type of container and placed in the sun for 30 minutes. The increase in temperature is given in the table. Study the table and answer the following questions:
I. Which liquid has the highest specific heat capacity? Why?
II. If equal mass of all the liquid at same temperature cooled, which one will cool faster? Why?
Ans: The specific heat capacity of a body is defined as the amount of heat required to raise the temperature of unit mass of that body by 1°C or 1K.
Different substances have different specific heat capacities. The bodies, which have more specific heat capacity, change their temperature slowly and those, which have less specific heat capacity, change their temperature faster.
I. The same amount of heat is applied to all three liquids for the equal time interval and liquid A has the lowest increase in temperature. As we know that, the substance which has more specific heat capacity, change their temperature slowly. So, the liquid A has more specific heat capacity.
II. If the equal mass of all three liquids at the same temperature is cooled, liquid C will cool faster, because the same amount of heat is applied to all three liquids for the equal time interval and liquid C has the highest increase in the temperature. That means liquid C has the lowest specific heat capacity and we know that substance which has less heat capacity, change their temperature faster.
14. If 200 gm. of water at 40°C is mixed with 2 kg of water at 30°C. Find the final temperature of the mixed water.
Here,
Given,
For hot water,
Mass (m1) = 200 gm. = 0.2 kg
Initial temperature (t1) = 40°C
For cold water,
Mass (m2) = 2 kg
Initial temperature (t2) = 30°C
Specific heat capacity (s) = 4200 J/kg°C
Final temperature of mixture (t) =?
According to the heat equation,
Q =msdt
where,
m = Mass of body
Q = Heat gained or lost
s = Specific heat capacity of the body
dt = Change in temperature
Again,
According to the principle of calorimetry, the amount of heat gained is equal to the amount of heat loss.
So,
Heat lost by hot water = Heat gained by cold water
m1sdt1 = m2sdt2
Or, 0.2 х 4200 х (40 — t) = 2 х 4200 х (t — 30)
t = 30.9°C
Hence, the final temperature of the mixed water is 30.9°C.
15. Hot water of mass 10 kg at 90°C cooled for taking bath by mixing 20 kg of water at 20°C. What is the final temperature of water? Specific heat capacity of water is 4200 J/kg°C? Neglect the heat taken by bucket?
Solution: Here,Given,For hot water,
Initial temperature (t1) = 90°C
For cold water,
Mass (m2) = 20 kg
Initial temperature (t2) = 20°C
Specific heat capacity (s) = 4200 J/kg°C
Final temperature of mixture (t) =?
According to the heat equation,
Q = msdt
where,
m = Mass of body
Q = Heat gained or lost
s = Specific heat capacity of body
dt = Change in temperature
Again,
According to the principle of calorimetry, the amount of heat gained is equal to the amount of heat lost.
So,
Heat lost by hot water = Heat gained by cold water
m1sdt1 = m2sdt2
Or, 10 х 4200 х (90 — t) = 20 х 4200 х (t — 20)
t = 43.33°C
Hence, the final temperature of the water is 43.33°C.
.
17.
I. The temperature of an iron nail of mass 2 kg is 50°C and water of mass 200 gm. is 80°C, then which one substance has more heat energy? Calculate (The specific heat capacity of water and iron is 4200 J/kg°C and 1470J/kg°C respectively).
II. If the iron nail is put in the water in which direction heat energy will flow and why?
Solution:
I.
Here,
Given,
For iron nail,
Mass (m1) = 2 kg
Temperature (t1) = 50°C
Specific heat capacity (s1) = 470 J/kg°C
Heat energy (Q1) =?
For water,
Mass (m2) = 200 gm. = .2 kg
Temperature (t2) = 80°C
Specific heat capacity (s) = 4200 J/kg°C
Heat energy (Q2) =?
According to the heat equation,
Q =mst
where,
m = Mass of body
Q = Heat energy of a body
s = Specific heat capacity of body
t = Temperature
Again,
For iron nail,
Q1 =m1s1t1= 2 х 470 х 50 = 47,000 J
For water,
Q2 =m2s2t2 = .2 х 4200 х 80 = 67,200 J
Hence, Water has more heat energy.
II.
If an iron nail is put in the water, heat energy will flow from water to iron. Because the heat energy always flows from the body having a higher temperature to a body having a lower temperature.
18. What is thermometer?
Ans: The thermometer is an instrument used for measuring a temperature of a body.
19. Water is not used as a thermometric liquid. Why?
Ans: Water is not used as a thermometric liquid because water has not uniform expansion as it contracts on heating from 0oC to 4oC and then expands on further heating from 4oC.
20. Write any three differences between clinical and laboratory thermometer.
Ans: The amount of heat required to raise the temperature of a whole body or substance through 1°C is called thermal heat capacity.
22. Derive Principle of caloriemetry
The principle of caloriemetry states,
“When two bodies of different temperatures are brought together, the body at higher temperature looses heat energy whereas the body at lower temperature gains heat energy. The process will continue until they reach at thermal equilibrium.”
The heat may get lost in external environment. But if the heat is not lost to external environment, then heat lost by body at higher temperature is equal to heat gained by body at lower temperature.
i.e Heat lost = Heat gained
This process continues until both bodies are at same temperature.
Let the mass of a body at higher temperature is m1, its specific heat capacity is s1 and the temperature of body is t1.
Similarly, let the mass of a body at lower temperature is m2, its specific heat capacity is s2and the temperature of body is t2.
If both bodies are brought together, then let the final temperature of the mixture be t.
If dt and dt’ are difference in temperature of bodies at higher and lower temperature respectively, then their values will be
dt = (t1 – t)
and
dt' = (t - t₂ )
So, the amount of heat energy lost by a body at higher temperature will be
Heat lost = m1s1dt
Similarly, the amount of heat energy gained by a body at lower temperature will be
Heat gained = m2s2dt'
Do you remember the principle of caloriemetry?
According to the principle of caloriemetry,
Heat lost = Heat gained
or, m1s1dt = m2s2dt'
or, m1s1 (t1 – t) = m2s2 (t – t₂)
23. What is heat?
According to the molecular theory, heat is the sum of total kinetic energy of the molecules of a body.
24. What is one Calorie?
25. What is the principle of caloriemetry?
26. What is heat equation?
27. On which factors does the heat lost or gained by a body depend?
28. Steam causes more burning than boiling water. Why?
29. On which factors does the heat content of a body depend?
30. Give reason:
II. A new quilt is felt warmer than old one.
Ans:
I. Water has very high specific heat capacity (4200 J/kg°C) as compared to other liquids. The substances which have more specific heat capacity change their temperature slowly. Thus, water can absorb large amount of heat from the hot engines without appreciable rise in temperature of water. So, it prevents the engines of vehicle being excessively hot. Due to this reason water is used to cool the engine of vehicles.
II. A quilt feels warm because the air trapped in between the cotton or woolen batting acts as an insulator and does not allow the heat of the body to escape. However, when the quilt gets old, the cotton/woolen batting gets compressed and air spaces decreases. It does not remain as good an insulator to heat as it was earlier. Hence, a new quilt is felt warmer than old one.
31. In the given diagram, 100 gm. water is kept in the first beaker and 100 gm. mustard oil is kept in the second beaker. Study the diagram and answer the following question:
II. Which one cool fast, if both have a temperature of 100°C and why?
III. Which conclusion can be drawn from this activity?
Ans: I. If an equal amount of heat is applied to both objects, mustard oil will have more temperature. Because it has lower specific heat capacity in comparison to water and the substance which has less specific heat capacity, change their temperature faster. So, the temperature of the mustard oil will increase faster in comparison to water.
II. The bodies, which have more specific heat capacity, change their temperature slowly and those, which have less specific heat capacity, change their temperature faster. If both have temperature 100°C, mustard oil will cool faster. Because it has less specific heat capacity in comparison to water.
III. The conclusion drawn from this activity is, 'Different substances have different specific heat capacities. The bodies, which have more specific heat capacity, change their temperature slowly and those, which have less specific heat capacity, change their temperature faster'.
32. How much heat is supplied to raise the temperature of 100 gram of water from 5°C to 90°C? (Specific heat capacity of water = 4200 Jkg-1 °C-1)
33. How much heat is required to raise the temperature of an aluminium kettle of mass 400 gram through 900C? (Specific heat capacity of aluminium = 899 Jkg-1 0C-1)
34. If 50 kJ of heat is transferred to 10 kg of water, what is the rise in its temperature? (Specific heat capacity of water is 4200 Jkg-1 °C-1)
35. Calculate the specific heat capacity of the alloy of which a pressure cooker of mass 1.5 kg is made of if the quantity of heat necessary to raise its temperature by 60°C is 81kJ.
36. If 200 ml of tea at 900C is mixed with 10 ml of milk at 150C, what will be the final temperature of the mixture? Assume that mass of 1 ml tea = mass of 1 ml milk = 1 gram and specific heat capacity of milk equals that of tea.
37. Derive Q = m × s × dt
let mass of a body is m and the heat required to deviate the body temperature by dt is Q.
Experimentally, it has been found that;
- Heat energy (Q) lost or gained by a body is directly proportional to the mass (m) of the body.
i.e. Q ∝ m ................ ¹
- Heat energy (Q) lost or gained by a body is directly proportional to the change in temperature (dt) of the body.
i.e. Q ∝ dt ..................... ²
Combining relations 1 and 2, we get,
Q ∝ m × dt
The heat energy changes by certain multiplying factor, Specific heat capacity of the body.
The value of 'm' is different for different bodies.
Hence, the relation becomes
Q = m × s × dt
Change in body temperature (dt) is given by the difference between two temperature of a body.
If t1 and t2 are initial and final temperatures of a body, then change in temperature is dt = t2 – t1
- If the value of t2 is greater than t1, then the value of dt is positive.
i.e. the body temperature has increased. So, it must mean that the body absorbed heat energy.
- If the value of t1 is greater than t2, then the value of dt is negative.
i.e. the body temperature has decreased. So, it must mean that the body lost its heat energy.
The value of energy is always positive. So if a body loose heat energy, the change in temperature is dt = t1– t2.
38. Specific heat capacities of three substances are given in the table. Answer the following questions observing the given table.
a) The specific heat capacity of substance ‘A’ is 910 J/kg°C, what does it mean?
b) Which one will gain the least temperature if equal heat is given to the equal masses of the three substances at equal temperature?
c) If equal masses of all three substances are heated upto 100°C and then kept on a wax slab, which one will go to the maximum depth in the wax slab?
d) If all of the substances are liquids, which one is suitable for using as a thermometric liquid?
Ans:
a) The specific heat capacity of the substance ‘A’ is 910 J/kg°C.
It means that we need to supply 910 Joule of heat to raise the temperature of 1 kg mass of substance ‘A’ at 1°C.
b) The substance having high specific heat capacity needs more heat to raise its temperature.
So, raise in temperature is slower in the substance having higher specific heat capacity.
Here, substance ‘C’ has the highest specific heat capacity.
Therefore, substance ‘C’ will gain the least temperature if equal heat is given to the equal masses of the three substances at equal temperature.
c) The substance having high specific heat capacity needs to lose more heat to fall its temperature.
So, cooling is slower in the substance having higher specific heat capacity.
Here, substance ‘C’ has the highest specific heat capacity.
Therefore, substance ‘C’ will remain hot for a long time when placed on the wax slab.
It can supply more heat to the wax during the cooling process and melts more wax.
So, substance ‘C’ will go to the maximum depth in the wax slab if equal masses of all three substances are heated up to 100°C and then kept on a wax slab.
d) The substance having less specific heat capacity gets heated faster with less heat.
So, it expands faster on heating.
The thermometric liquid should be highly heated sensitive.
It should expand quickly while measuring the temperature.
Here, substance “B” has the least specific heat capacity.
It expands faster than the other substances.
So, liquid “B” is suitable for use as a thermometric liquid.
39. What is specific heat capacity?
Ans: Specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of 1 kilogram of the substance through 1°C.