Scenario
You are working as a field engineer on a remote construction project in Siberia. Your manager
has asked you to perform several thermodynamic calculations to understand different aspects
of the project in the extreme temperatures.
Task 1
a) A suspension bridge is being installed that must be able to operate in extreme cold of -40oC. If
the bridge was fabricated in 20oC conditions, what change in length can be expected in the longest
steel cable of 40m? The coefficient of linear expansion of steel is 12x10-6 oC-1
.
b) With the frigid temperatures, it is more feasible to supply ice than water. Your manager plans to
procure fuel to melt the ice and heat it to the necessary temperature of 10oC. In order to
determine amount of fuel needed per day, your manager has asked you to calculate the heat
energy required to produce 4 tonnes of water (at the ideal 10
oC) from ice at the average
temperature of -15oC. Use the following values:
• Specific heat capacity of ice as 2.0 𝑘𝐽
𝑘𝑔∙𝐾
• Specific heat capacity of water as 4.2
𝑘𝐽
𝑘𝑔∙𝐾
• Specific latent heat of fusion as 335 𝑘𝐽
𝑘𝑔
This provides evidence for [P8]
Task 2
a) The tube of an equipment tyre is filled with 5 kg of air to a pressure of 35 MPa at a temperature of
40°C. The tyres tubes contract by 15% when the equipment is moved to a location with a
temperature of -20°C. After the equipment has been operating for a period of time, the tyre
pressure reads 370 bar. Determine the following:
i. Initial volume of the tyre tube
ii. Pressure inside the tyre after the initial move (at -20°C with the contracted volume)
iii. Temperature inside the tyres after they have been operating, assuming the contracted
volume remains constant and no additional air is added.
For air, take R=287 𝐽
𝑘𝑔∙𝐾
.
b) Underwater welding work must be undertaken. A 15 L tank is filled to 135 bar compressed air at
a temperature of 20°C. The work will be undertaken at 30 m depth, at approximate conditions of
4 bar and 5°C. The work takes half an hour, and the welder breathes approximately 6 Lpm (Litres
per minute). The pressure of air in the lungs will equalise with the external water pressure.
Determine the following:
i. Initial mass of the air
ii. Initial tank pressure in working conditions.
iii. Mass of air used by the welder
iv. Final pressure in the tank, assuming isothermal conditions.
For air, take R=287 𝐽
𝑘𝑔∙𝐾
.
This provides evidence for [P9]
Task 3
The water production system has been installed successfully, with a fuel source of coal. Your manager
has decided to add a secondary system to produce hot water at 60oC from the cold water at 10oC. The
hot water system is only run for certain periods of the day and produces .2 tonnes per hour of hot water.
If 5 kg of coal per hour is needed to heat water to the desired temperature, calculate the thermal
efficiency of the process. The calorific value of coal is 40 MJ/kg, and the specific heat capacity of water is
4.2 kJ/(kgK).
Sample Solution