A chef cooks a 4 ounce steak (0.12 kg). The meat is freshly removed from a 10 C

Question

A chef cooks a 4 ounce steak (0.12 kg). The meat is freshly removed from a 10 C refrigerator and put on the grill. The power of the grill is 400 W. To be able to serve the meat the steak needs to be heated to a temperature of 80 C. The specific heat of this cut of meat is 3200 J/kg. What is the energy required to get the steak up to the required temperature? How long will it take to get the steak up to the required temperature? For some reason the steak is a perfect sphere with a radius of 5 cm (0.05 m). If 80 C is 352 K then how much power does the steak radiate when it is heated to 80 C? Do we buy new windows? Imagine you have 10 windows in a house and each window has an average square are of 2.1 square meters. Imagine these windows while double paned are a bit older so their R value is only 2. You are considering upgrading to R = 6 windows that cost about $800 each (which is expensive for windows). However, is it worth it, lets find out! Let us assume that the average temperature difference between the inside and the outside over the course of the year is 15 C. For R=2 and R=6 find how much energy passes through the set of 10 windows over the course of a year (1 year = 3.16 multiplication 10^7 sec). If on average 500, 000 J costs 1 cent (or $1 = 5 multiplication 10^7 J) then how much money goes out the windows each year (do for both R = 2 and R = 6 windows)? How long would it take you to save back the $8k it would cost to replace your 10 windows? Is this worth it, why or why not?

Explanation / Answer

1. a)

q = mcdT

= 0.12*3200*(80-10)

26880 J

b)

T = Q/P

= 26880/400

=67.2 SEC0ND.

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