PHYC20012 Assignment 1
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
PHYC20012 Assignment 1
Instructions
It is expected that this assignment will take about 8 hours of work to complete. The format of the report is expected to be consistent with this time commitment which means an artistically presented report with colourful diagrams is NOT expected.
There is no restriction on the sources of information you may use to answer the questions in this assignment, but it is essential that you report all the references you consulted for your
work. Be sure to show your working and state any assumptions you make. The theory for this assignment will be covered in lectures 1 to 12.
Please follow the instructions on the LMS to submit your assignment by the due date. Attach the signed coversheet (previous page) to the front of your assignment.
This is “Assignment 1” (10% of final marks) as described in the handbook.
The total number of marks is 100. You may assume the amount of detail expected in the answers is proportional to the allocated marks.
Submit your assignment as a pdf file using the link provided on the LMS. Be sure to include the cover sheet on the previous page as page 1 of your submission.
Note that this LMS submission link will be disabled automatically by the LMS system at the
deadline for submission.
Submission Deadline Friday April 1 at 5 pm
This is the last possible time to submit the assignment. Please don’t leave it to the last minute to submit!
(Questions start on the next page)
Question 1 – (8+10+10+8=36) marks
Heating semiconductor wafers is part of the process used to make semiconductor devices.
(a) Define the concept of specific heat capacity at constant volume, , and constant
volume, . For a solid, explain why these two values are usually approximately the same, but why they differ greatly for a gas.
(b) A silicon wafer of mass 0.010 initially at a temperature of 20℃ is heated to 900℃
in a furnace. Using the data provided in the figure ON THE NEXT PAGE, calculate the increase in internal energy of the wafer. Hence calculate the change in entropy of the silicon wafer.
(c) A diamond crystal of mass 0.010 g is subject to the same thermal treatment. Once again use the data in the figure ON THE NEXT PAGE to calculate the increase in internal energy and hence the change in entropy of the crystal.
(d) Provide a qualitative physical explanation for the differences in your results with reference to the Einstein model.
Question 2 – (8+8=16) marks
(a) Enthalpy: Look up the definition of “Standard Enthalpy” and “Enthalpy of Formation”
then provide a brief synopsis of how each concept is defined and give one application by way of example.
(b) In model rocketry, a popular but dangerous propellant is the oxidation of sugar
(sucrose, 112211) with potassium perchlorate (3 ). The chemical reaction is:
112211 + 83 → 122 + 112 + 8 The enthalpy of formations (at 1 , 273 ), , are:
Substance |
State |
(/ ) |
|
|
−2221 |
3 |
|
−430 |
2 |
|
−293.5 |
2 |
|
−241.8 |
|
|
−436.7 |
How much heat is produced by this chemical reaction? What is the significance of the sign of your answer?
The data in each graph has been fitted with two linear equations over the temperature ranges shown in the figure. Each equation has the form
= + .
where and are constants with units −1 −1 and −2 −1 respectively. The break between the two equations is shown by the dashed line at the given temperature.
Question 3 – (8+10+6+8=32) marks
Consider a packet of energy, ∆ , that is emitted by the Sun in the form of sunlight and is absorbed by the Earth. Seen from the Sun the Earth subtends a disk of radius and area . At the mean distance from the Sun to the Earth, 1,370 passes through every square metre every second. That is, the disk subtended by the Earth is irradiated by a power density of = 1,370 /2.However only a fraction of this power is absorbed because a fraction is reflected back into space with the fraction given by the albedo, . The power actually absorbed is therefore (1 − ) . Let ∆ be the amount of energy that is emitted by the Sun and absorbed by the Earth over an area of d = 1 2 in a time of d = 1 so that
|∆| = (1 − ) . d . d = 945
This problem is to track the entropy associated with the passage of ∆ from the Sun to the Earth until it is dissipated into deep space as radiant heat.
(i) To start this problem, first look up the Stefan-Boltzmann Law (sometimes just called “Stefan’s Law”) and provide an explanation of how the law relates the power density emitted by a hot object to the object’s temperature.
(ii) Use the Stefan-Boltzmann Law to calculate the average temperature of the Earth. You
can assume the Earth is equilibrium and the same amount of energy absorbed from the Sun is then re-radiated isotropically into space. This result is called the “Theoretical Black-Body Surface Temperature” (TBBST).
(iii) This calculation was first performed by Nobel Laureate Svante Arrhenius. He
recognised that the result was an underestimate because the calculation neglected the Greenhouse Effect. Construct a table of TBBST calculations for the planet Venus, Earth and Mars (see example on next page). Use a suitable reference to look up the actual average surface temperature of the three planets. Provide a qualitative explanation for the similarity, or otherwise, of the TBBST and the actual surface temperatures of the three planets.
(iv) Considering the temperature of the surface of the Sun[*], the average temperature of
the Earth from (iii), the temperature at the top of Earth’s atmosphere where heat is radiated to space[*] and the temperature of deep space [*] make a table showing the entropy change associated with the transfer of ∆ as it passes from the Sun through the Earth to its ultimate fate in deep space. What do you conclude about the sign of the result for the origins of life on Earth? Here [*] indicates you will need to look up these values in the literature and justify your choices.
Here is a suggested table for presenting you results from part (iii) with some numbers filled in for you.
Data and Results |
Mars |
Earth |
Venus |
Albedo, |
0. 17 |
0.31 |
0.78 |
Planet radius, () |
|
|
|
Distance from Sun () |
|
|
|
Solar irradiance (/2) |
|
1370 |
|
Theoretical Black Body Surface Temperature TBBST calculated from the Stefan-Boltzmann Law () |
|
|
|
Actual average surface temperature from the literature () |
|
|
|
|∆| = (1 − ) . d . d |
|
945 |
|
Here is a suggested table for presenting the results in part (iv) with some numbers filled in for you.
Object |
Surface Temperature () |
Energy, () |
Entropy, ∆ (/) |
Radiation from Sun |
|
−945 |
|
Absorption by Earth |
|
|
|
Radiation by Earth |
|
|
|
Absorption by deep space |
3 |
|
|
TOTAL |
|
0 |
|
Be sure to provide references for the source of your data needed for this table.
Question 4 – (16) marks
Engines that power light aircraft burn hydrocarbon liquid fuels. The liquid fuel is converted to vapour and mixed with air to form an explosive mixture which is injected into the cylinders of the engine where it burns to provide propulsion. The conversion of the liquid fuel to fuel vapour occurs by passing the liquid through a small aperture, called a jet, where the liquid rapidly expands in volume and becomes vapour just before it is mixed with air.
A hazard associated with this process is that the fuel can become contaminated when water from humid air dissolves in the fuel. In some circumstances it is found that the rapid expansion from the jet causes the dissolved water to freeze and block the intake into the engine which can cause the engine to stop working owing to fuel starvation. In very humid air, the water vapour in the air can freeze even if the fuel is not contaminated with water.
With reference to the appropriate quasistatic process, explain qualitatively why the water in the fuel cools sufficiently to freeze. Explain why the problem is particularly likely to occur when the intake to the engine is already partially blocked by a throttle valve used to reduce the rate of engine fuel intake and hence the speed of the engine during landing.
Be sure to cite any references you consult, especially if you choose to include a diagram in your answer or reference the freezing temperature of JET-A1 fuel.
2022-03-30