Question

Generate and provide your answers to ALL questions using a Microsoft Excel Worksheet(s) and submit this Worksheet as a separate document with your Word document file.

Note: You may answer this question in two or more Excel Worksheets – one Worksheet containing the table and the other Worksheet containing all the plots. Alternatively, you may choose to provide each plot in a separate Worksheet.  

Demonstrate how the spectral emissive power inside a blackbody cavity changes with respect to the following parameters:

Temperature and wavelength, hence, find Eλ(λ, T), by:

a) Creating a table with the (λ, T) values as follows:

1. Wavelengths, λ, from 0.1 μm to 100 μm, on the first (left-most) column. Use increments of:  

→ 0.1 μm from 0.1 μm to 1.0 μm;  

→ 0.5 μm from 1.0 μm to 10 μm;

→ 1.0 μm from 10 μm to 100 μm;

2. Temperatures, T, values of: 293.15 K; 793.15 K; 1293.15 K; 1793.15 K; 2293.15 K; 7500 K; and, 12000 K.

3. Calculate Eλ(λ, T) using units of W/m2·μm and assume the constants C1 = 374210000 and C2 = 14388.  

Set up your table with each separate column corresponding to each given value of T. Ensure that you clearly label each column in your table and include the relevant units.

[Hint: There should be seven separate columns in your table for the Eλ(λ, T) calculations and eight columns in your table altogether with the inclusion of the left-most column consisting of the λ values.

The recommendation is that you fill in each separate column in your table using a different background colour in order to facilitate the examination of the different T calculations and to assist in identifying the corresponding plots.]

4. Clearly demarcate the visible region in your table. You may do this by selecting a different coloured font for the values of λ (and the corresponding Eλ values) that fall within this region.

b) Plot the calculated values of Eλ(λ, T) ensuring that you set out each plot as follows:

1. Display the calculated Eλ(λ, T) values on the vertical axis.

2. Display the wavelengths on the horizontal axis. Select the logarithmic scale, to base 10, to display your values on this axis.

3. Clearly demarcate the visible region in each plot.

4. Include a title in each plot, clearly identifying the relevant value of T and ensure that you label both axes (including units).

[Hint: The recommendation is that you fill in the background of each plot in the same colour as the corresponding column in your table in order to facilitate the analyses of the different T calculations.]

Answer 1

4. The visible range is from 0.4 micron to 0.7 micron

plot for 293.15 K, hatched area is in visible region

for 793 K

The visible range of wavelength has been either hatched or highlighted.