1. Explain what is meant by heat. State the zeroth law of thermodynamics and show how
the concept of temperature follows from it.
2. A block of copper of mass 0.50 kg at an initial temperature of 77°C is placed in 0.40
kg of water at 30°C. When thermal equilibrium is attained, the temperature of the
mixture is 35°C. How much heat is lost by the copper block and how much heat is
absorbed by the water?
Comment on your answers.
(specific heat capacities: water = 4 200 J kg −1 K −1 , copper = 400 J kg −1 K −1 )
Solution:
Heat lost form copper block = 𝑚𝑐 𝑑𝑇
= 0.50 × 400 × (77 − 35)
= 8 400 J
Heat gained by water = 𝑚𝑐 𝑑𝑇
= 0.40 × 4 200 × (35 − 30)
= 8 400 J
∴ heat gained = heat lost
Which is consistent with the principle of conservation of energy.
3. The specific heat capacity of a solid at temperatures close to 0 K is given by 𝑐 = 𝑘𝑇 3
where T is the temperature and k is a constant characteristic of the solid.
Find the heat required to raise the temperature of such a solid o f mass m from a
temperature of 𝑇1 to 𝑇2
4. The temperature of a hot liquid in a container of negligible thermal capacity falls at a
rate of 2°C per minute just before it begins to solidify. The temperature then remains
steady for 20 minutes by which time the liquid has all solidified.
5. What is the value of the ratio?
specific heat capacity of liquid
?
specific latent heat of fusion
Solution:
Let 𝑚 = mass of liquid
From the equation 𝑑𝑄 = 𝑚𝑐 𝑑𝑇
∴ rate of heat loss
𝑑𝑄
𝑑𝑡
𝑑𝑇
= 𝑚𝑐 𝑑𝑡
= 𝑚𝑐(2)
If 𝐿 = specific latent heat of fusion when the liquid completely solidifies,
Heat loss = 𝑚𝐿
∴ rate of heat loss
𝑑𝑄
𝑑𝑡
𝑚𝑐(2) =
= (2)
C
1
∴ L = 40
𝑚𝐿
20
𝑚𝐿
20
=
= 0.025 K −1
6. A solid object of mass M is made from material of specific heat capacity 𝑐, of
specific latent heat of fusion L and of very high thermal conductivity. When the
object enters the atmosphere from outer space, its temperature is below its melting
point by ∆T. Because of atmospheric friction, it absorbs energy at a constant net rate
of R. What is the time before the solid becomes completely molten?
Solution:
𝑑𝑄 = 𝑚𝑐 𝑑𝑇
Heat required to raise the temperature of the solid to its melting point = 𝑀𝑐 ∆𝑇
Heat require to completely melt all the solid, 𝑄 = 𝑀𝐼
∴ total heat required = 𝑀𝑐 ∆𝑇 + 𝑀𝑙
Rate of heat absorption = 𝑅
total heat required
rate of absorption
𝑀𝑐 ∆𝑇+𝑀𝑙
=
𝑅
𝑀(𝑐 ∆𝑇+1)
=
𝑅
∴ time required =
7. A lagged copper rod has a uniform cross-sectional area of 1.0 cm2 and length 20.0
cm. when steady state is attained, the temperature of one end of the rod is 120°C
and the other end is 0°C. Find
(a) The temperature gradient.
(b) Rate of heat flow,
(c) The temperature at a point 8.0 cm from the hot end.
(d) The temperature at a point 8.0 cm from the hot end.
(thermal conductivity of copper = 380 W m−1 K −1 )
Solution
(a) Temperature gradient =
0−120
20.0
𝑑𝜃
𝑑𝑥
= −6.0°C cm−1
= −600°C m−1
𝑑𝜃
(b) Rate of heat flow = −𝜆Α 𝑑𝑥
= 380 × (1.0 × 10−4 ) × 600
= 22.8 W
(c) Temperature at a distance of 8.0 cm from the hot end = 120 + (−6 × 8.0)
= 72°C
8. Window glass has a thermal conductivity of 0.80 W m−1 K −1. Calculate the rate at which
heat is conducted through a window of area 2.0 m2 and thickness 4.0 mm if the temperature in an airconditioned room is 20°C and the outdoors temperature is 35°C.
This calculation over-estimates the rate of heat flow by a substantial amount. Suggest a reason for this.
Solution
Rate at which heat is conducted,
𝑑𝑄
𝑑𝑡
𝑑𝜃
= −𝜆Α 𝑑𝑥
(35−20)
= 0.80 × 2.0 × 4 × 10−3
= 6.0 × 103 W
The answer is an over-estimate because it is assumed that the temperature of the outside surface of the
glass is the same as the outside temperature and the temperature of the inside surface of the window is
the same as the room temperature. In practice the layer of still air outside, next to the window is cooled
by the window. Hence the temperature gradient across the window is actually lower and the rate of
heat flow would be smaller.
9. A uniform rod of cross-sectional area 90 mm2 is made of a metal of thermal
conductivity 0.31 kW m−1 K −1. One end of the rod is maintained at a high constant temperature.
When a steady state is attained, the temperature gradient at two cross- sections along the rod is 4.6 ×
102 K m−1 respectively. Calculate the mean rate of heat loss from the sides of the rod between the two
points.
Solution;
Rate of heat flow across the first cross-section
𝑑𝑄
𝑑𝜃
( 𝑑𝑡 ) = 𝜆Α(𝑑𝑥 )1
Rate of heat flow across the second cross-section`
𝑑𝑄
𝑑𝜃
( 𝑑𝑡 )2 = −𝜆𝐴(𝑑𝑥 )2
∴ mean rate of heat loss from the sides of the rod
𝑑𝑄
𝑑𝑄
𝑑𝜃
𝑑𝜃
( 𝑑𝑡 )1 − ( 𝑑𝑡 )2 = 𝜆Α(𝑑𝑥 )1 − (−𝜆Α(𝑑𝑥 )2
= −(0.32 × 103 )(90 × 10−6 )(4.6 − 2.8)102
= −5.18 W
9.
10.
11.
12.
13.
A vacuum flask is closed with a cylindrical stop of diameter 10.0 cm and thickness 2.5 cm. it
contains 1.00 kg of ice at 0°C. When the temperature on the outside is 20°C, it is found that all
the ice in the flask melt in 30 hours. What is the mean temperature on the inner side of the
stopper if heat transferred into the flask is only via the stopper (Specific latent heat of fusion of
ice = 3.35 × 105 J kg −1 , thermal conductivity of stopper = 0.67 W m−1 K −1)
If an electric oven at a temperature of 800 K is assumed to be a black body radiator, what is the
frequency of the radiation emitted with the highest intensity by the oven?
[Wien’s constant =2.9×〖10〗^(-3) m K]
A point charge q1 = 2.0 μC is located on the positive y axis at y = 0.30 m and an identical charge
q2 is at the origin. Find the magnitude and direction of the total force that these two charges
exert on a third charge q3 = 4.0 μC that is on the positive on positive x axis at 1 x = 0.40 m
A student uses a ripple tank where all the water is the same depth. She measures the
wavelength of each wave as 0.34 m.The period of each wave is 0.42 s. Calculate the speed of the
wave. Give the unit. Give your answer to three significant figures
Reaction: N2 + 2O2 → 2NO2
The following data were obtain:
Experiment
[O2] mol/L
[N2] mol/L
Initial rate mol/L/s
1
0.001
0.025
0.0005
2
0.002
0.025
0.0020
3
0.002
0.050
0.0160
Determine the order of the reaction w.r.t. each reactant. [10 mark]
Write the rate law for the above reaction.
Calculate the rate constant, k, and give its appropriate units
14. Define the following terms as applied in thermodynamics:
Adiabatic process
Quasistatic or Quasi-equilibrium process
Specific properties
Isobaric process
(β) What are the intensive and extensive properties?