Download PHY2216: Tutorial Questions 5 TEMPERATURE 5.1 Temperature

PHY2216: Tutorial Questions 5
TEMPERATURE
5.1
Temperature Scales:
1.
The distance between the fixed points of a Celsius thermometer is 20cm. What is the
temperature when the mercury level is 4.5cm above the lower mark?
[Answer: 22.5oC]
2.
Find the temperature at which the Celsius and Fahrenheit thermometers have the same
reading.
[Answer: – 40oC]
3.
A thermometer has its stem marked in millimeter instead of degree Celsius. The lower
fixed point is 30mm and the upper fixed point is 180mm. Calculate the temperature in
degree Celsius when the thermometer reads 45mm.
[Answer: 10oC]
5.2
Thermometers:
4.
The resistance of platinum is 5.684Ω at the temperature of steam at 760mm mercury and
5.240Ω at the temperature of melting ice. If the resistance at the temperature of a warm
liquid is 5.490Ω, calculate the liquid temperature.
[Answer: 56oC]
5.
A particular resistance thermometer has a resistance of 30.00  at the ice point, 41.58 
at the steam point and 34.59  when immersed in a boiling liquid. A constant-volume
gas thermometer gives readings of 1.333 x 105 Pa, 1.821 x 105 Pa and 1.528 x 105 Pa at
the same three temperatures. Calculate the temperature at which the liquid is boiling:
(i)
on the scale of the gas thermometer,
(ii)
on the scale of the resistance thermometer.
[Answer: (i) 39.96oC (ii) 39.64oC]
6.
The resistance R of a particular resistance thermometer at a Celsius temperature  as
measured by a constant-volume gas thermometer is given by:
R = 50.00 + 0.1700 + 3.00 x 10-42
Calculate the temperature as measured on the scale of the resistance thermometer which
corresponds to a temperature of 60oC on the gas thermometer.
[Answer: 56.40oC]
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7.
Show that the Celsius temperature  corresponding to a length  of the mercury column
is given by:
 0
 
x.100
100  0
where 0 and 100 are the lengths of the mercury column at 0oC and
100oC respectively.
8.
A resistance thermometer has a resistance of 21.42  at the ice point, 29.10  at the
steam point and 28.11  at some unknown temperature . Calculate  on the scale of this
thermometer.
[Answer: 87oC]
9.
A particular constant-volume gas thermometer registers a pressure of 1.937 x 104 Pa at
the triple point of water and 2.618 x 104 Pa at the boiling point of a liquid. What is the
boiling point of the liquid according to this thermometer?
[Answer: 369.2K]
10
The temperature measurement described in question 9 was repeated using the same
thermometer but with a different quantity of (the same) gas. The readings on this
occasion were 4.068 x 104 Pa at the triple point of water and 5.503 x 104 Pa at the boiling
point of the liquid.
(a)
What is the boiling point of the liquid according to this measurement?
(b)
Which of the two values is the better approximation to the ideal gas temperature,
and why?
(c)
Estimate the ideal gas temperature.
[Answer:
(a) 369.5K (b) 369.2K (because it is measured at a lower pressure (c)
368.9K]
11.
The pressure on the gas of a constant gas thermometer at the ice point is 325mm of
mercury and at the steam point 875mm of mercury. Find the temperature when the
pressure of the gas is 490mm of mercury.
[Answer: 303K]
5.3
Heat Capacity:
12.
Calculate the quantity of heat required to raise the temperature of a metal block with a
heat capacity of 23.1 JoC-1 by 30.0oC.
[Answer: 693J]
13.
An electrical heater supplies 500 J of heat energy to a copper cylinder of mass 32.4 g.
Find the increase in temperature of the cylinder. (Specific heat capacity of copper = 385J
kg-1 oC-1.)
[Answer: 40.1oC]
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14.
How much heat must be removed from an object with a heat capacity of 150 JoC-1 in order
to reduce its temperature from 80.0oC to 20.0oC?
[Answer: 9.00 x 103J]
15.
A metal block of heat capacity 36.0 J oC-1 at 70oC is plunged into an insulated beaker
containing 200 g of water at 18oC. The block and the water eventually reach a common
temperature of oC.
(a)
Write down expressions in terms of  for:
(i)
the decrease in temperature of the block,
(ii)
the increase in temperature of the water.
(b)
Find in terms of :
(i)
the heat lost by the block,
(ii)
the heat gained by the water.
(c)
Assuming that no heat is lost to the surrounding, find the value of .
(Specific heat capacity of water = 4.2 x 103 J kg-1 0C-1.)
[Answer:
(a) (i) (70 – θ)oC (ii) (θ – 18)oC (b) (i) 36(70 – θ)J (ii) 840(θ – 18)J (c)
20.1oC]
16.
A given quantity of heat increases the temperature of 150 grams of water from 90C to
150C and increases the temperature of an equal volume of oil weighing 100 grams from
90C to 250C. Calculate the ratio of the specific heat of oil to that of water.
[Answer: 0.56]
17.
A heating coil of resistance 30Ω is connected to a 240V supply for 5 minutes to boil a
quantity of water in a vessel of heat capacity 200JK–1. If the initial temperature of the
water is 200C and its specific heat capacity is 4.2 x 103kg–1K–1, calculate the mass of
water in the vessel.
[Answer: 1.67g]
18.
A piece of copper of mass 120g is heated in an enclosure to a temperature of 1250C. It is
then taken out of the enclosure and held in the air for half a minute and dropped carefully
into a copper calorimeter of mass 105g containing 200g of water at 200C. The
temperature of the water rises to 250C. Calculate the rate at which heat is being lost from
the piece of copper when it is held in air.
(Specific heat capacity of water = 4200Jkg–1 0C–1, Specific heat capacity of copper =
400Jkg–1 0C–1)
[Answer: 13Js–1]
19.
250g of lead at 1700C is dropped into 100g of water at 00C. If the final temperature is
120C, calculate the specific heat of lead,
(Specific heat capacity of water is 4200Jkg–1 0C–1)
[Answer: 127.6Jkg–1 0C–1]
20.
An electric current 3A flowing through an electric heating element of resistance 20Ω
embedded in 1000g of an oil raises the temperature of the oil by 100C in 10 seconds.
Calculate the specific heat capacity of the oil.
[Answer: 0.18Jg–1 0C–1]
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5.4
Latent Heat:
21.
A calorimeter with a heat capacity of 80 J0C-1 contains 50g of water at 400C. What mass
of ice at 00C needs to be added in order to reduce the temperature to 10oC? Assume no
heat is lost to the surroundings. (Specific heat capacity of water = 4.2 x 103 J kg-1 0C-1,
specific latent heat of ice = 3.4 x 105 J kg-1.)
[Answer: 23g]
22.
Calculate the heat given out when 600 g of steam at 100oC condenses to water at 20oC.
(Specific latent heat of steam = 2.26 x 106 J kg-1, Specific heat capacity of water = 4.2 x
103 J kg-1 0C-1.)
[Answer: 1.56 x 106J]
23.
Calculate the heat required to melt 200 g of ice at 0oC.
(Specific latent heat of ice = 3.4 x 105 J kg-1.)
[Answer: 6.8 x 104J]
24.
Calculate the heat required to turn 500 g of ice at 00C into water at 100 oC.
(Specific latent heat of ice = 3.4 x 105 J kg-1,
Specific heat capacity of water = 4.2 x 103 J kg-1 0C-1.)
[Answer: 3.8 x 105J]
25.
A calorimeter contains 600g of water and 100g of ice at 00C. A piece of hot metal of
mass 1 kg is gently added to the mixture in the calorimeter and this causes all the ice just
to melt. Calculate the initial temperature of the metal. (Specific heat capacity of water =
4.2 x 103 J kg-1 0C-1, specific heat capacity of the metal = 4.2 x 102 J kg-1 0C-1, specific
latent heat of fusion of ice = 3.36 x 105 J kg-1 0C–1)
[Answer: 800C]
26.
0.5kg of water at 100C is completely converted to ice at 00C by extracting 188000J of
heat from it. If the specific heat capacity of water is 4200J kg-1 0C-1, calculate the specific
latent heat of fusion.
[Answer: 334000J kg-1]
27.
Calculate the amount of heat required to convert 2 kg of ice at –20C to water at 00C.
(Specific heat capacity of ice = 20904 J kg-1 0C-1, specific heat of fusion of ice = 333 x
1000 J kg-1)
[Answer: 6743360 J]
28.
All the heat generated in a 5Ω resistor by 2A flowing for 30 seconds is used to evaporate
5g of liquid at its boiling point. Calculate the specific latent heat of the liquid.
[Answer: 120Jg–1]
29.
A piece of copper of mass 300g at a temperature of 9500C is quickly transferred to a
vessel of negligible thermal capacity containing 250g of water at 250C. If the final steady
temperature of the mixture is 1000C, calculate the mass of the water that will boil away.
(Specific heat capacity of copper = 400 J kg-1 0C-1, specific heat capacity of water = 4.2 x
103 J kg-1K-1, specific latent heat of vaporization of steam = 2.26 x 106 J kg-1)
[Answer: 0.0102876 kg or 10.3g]
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30.
A piece of copper of mass 50g at temperature of 2500C is placed in a copper calorimeter
of mass 70g containing 60g of water at temperature of 200C. Ignoring heat losses, what
will be the final steady temperature of the mixture?
(Specific heat capacity of copper = 400 J kg-1K-1, specific heat capacity of water = 4.2 x
103 J kg-1K-1)
[Answer: 35.30C]
31.
All the heat generated by a current 2A passing through a 6Ω resistor for 25 seconds is
used to evaporate 5g of a liquid at its boiling point. What is the specific latent heat of the
liquid?
[Answer: 120Jg-1]
5.5
Expansivity:
32.
Steel bars, each of length 3m at 29o are to be used for constructing a rail line. If the linear
expansivity of steel is 1.0 x 10–5K–1, calculate the safety gap that must be left between
successive bars if the highest temperature expected is 41oC.
[Answer: 3.6 x 10–4m]
33.
A brass measuring rule is correct at 15oC. The volume obtained when the length of an
object is measured with the rule at 35oC appears to be 841.4cm. What is the true length of
the object? (Linear expansivity of brass = 1.8 x 10–5 oC–1)
[Answer: 841.1cm]
34.
A steel plug has a diameter of 5cm at 30oC. At what temperature will it fit exactly into a
hole of constant diameter 4.997cm? (Coefficient of linear expansivity of steel = 11 x 10–6
0 –1
C )
[Answer: – 24.6oC]
35.
Calculate the increase in volume when 1500cm3 of steel is heated from 0oC to 40oC.
(Coefficient of linear expansivity = 1.2 x 10–5 0C–1)
[Answer: 2.16cm3]
36.
The length of a side of a metallic cube at 200C is 5.0cm. Given that the coefficient of
linear expansivity of the metal is 4.0 x 10–5K–1, find the volume of the cube at 1200C.
[Answer: 126.50cm3]
37.
If the apparent cubic expansivity of a liquid in a glass container is 0.00070C–1, what mass
of the liquid will over-flow from a specific gravity bottle, filled to the brim with 100g of
the liquid at 300C, when its temperature is raised to 1000C?
[Answer: 4.67g]
38.
A brass rod is 2m long at a certain temperature. What is the length for a temperature rise
of 100K, if the linear expansivity of brass is 18 x 10–6 K–1?
[Answer: 2.0036]
39.
Define specific heat capacity, and specific latent heat of a substance.
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40.
What are the particular advantages of a continuous flow method in calorimetry.
41.
What is meant by the statement:
“The linear expansivity of a solid is 1.0 x 10–5K–1”?
42.
In order to establish a temperature scale, it is necessary to make use of fixed points. List
and describe three such points.
43.
Explain the meaning of Apparent Cubic Expansivity.
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