An egg, which for the purposes of this problem can be assumed to be a 5-cm-diameter sphere having the thermal properties of water, is initially at a temperature of 4°C. It is immersed in boiling water at 100°C for 15 min. The heat transfer coefficient from the water to the egg may be assumed to be 1700 W/(m2 K). What is the temperature of the egg center at the end of the cooking period?

GIVEN

An egg is immersed in boiling water

Initial temperature (To) = 4°C

Temperature of boiling water (T?) = 100°C

Time that the egg is in the water (t) = 15 min. = 900 s

The heat transfer coefficient (hc) = 1700 W/(m2 K)

FIND

The temperature of the egg center at the end of the cooking period

ASSUMPTIONS

The egg is a sphere of diameter (D) = 5 cm = 0.05 m

The egg has the thermal properties of water



SKETCH


The Biot number for the egg is



Therefore, the internal resistance is significant. Approximate solution can be used to solve the problem. The Fourier number at t = 900 s is



Using approximate solution, we have



For the center r=0, the term becomes indeterminate, so using L Hospital’s rule we get.



For Bi=62.3 which can be considered ? sphere we have

Physics & Space Science

You might also like to view...

A certain engine extracts 1300 J of heat from a hot temperature reservoir and discharges 700 J of heat to a cold temperature reservoir. What is the efficiency of this engine?

A) 46% B) 54% C) 86% D) 27% E) 13%

Physics & Space Science

In addition to the asteroid belt, some meteorites come from the Moon and even Mars

Indicate whether the statement is true or false

Physics & Space Science

Daisy raises 10.Kg to a height of 2.5 meters in 2.0 seconds

(a) How much work did she do? (b) How much power was expended? (c) If she raises it in 1.0 s rather than 2.0 s, how do the work and power change?

Physics & Space Science

Light from a gas discharge tube gives a (an) ________ spectrum

A) continuous B) absorption C) blackbody D) emission

Physics & Space Science