# A copper sphere of diameter 5 cm is initially at temperature 200°C. It cools in air by convection…

A copper sphere of diameter 5 cm is initially at temperature 200°C. It cools in air by convection and radiation. The temperature T of the sphere is governed by the equation here ρ is the density of copper, C its specific heat, V0 the volume of the sphere, t the time, ε a property of the surface known as emissivity, σ a constant known as the Stefan–Boltzmann constant, T∞ the ambient temperature, A the surface area of the sphere, and h the convective heat transfer coefficient. The initial condition is as follows: At t I = = 0 : 200°C Using Heun’s method, without iteration, solve this differential equation to find the temperature variation with time, until the temperature drops below 50°C. Use the following values: ρ ε σ = = = = × − ∞ 9000 5 67 10 8 4 kg/m 400 J/kg K 0.5 W/m K 3 2 C . T = ° 25 C h = 15 W/m2 K Employ time steps of 0.5 and 1.0 min, and compare the results obtained in the two cases.

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.