Problem 1: Toasters, blow dryers, and electric space heaters do their jobs via e
ID: 1275091 • Letter: P
Question
Problem 1: Toasters, blow dryers, and electric space heaters do their jobs via electric resistance heating: when electricity flows through a high-resistance wire, the temperature of the wire goes up, and heat is dissipated from the wire to the surroundings. A particular toaster uses 20 feet of a Nichrome resistance wire to cook toast. The diameter of the wire is 0.0285 inches.
a. Estimate the radiant heat transfer from the wire. You can assume that the surface temperature of the wire is approximately 750°C and that the wire is a thermal black body.
b. About how much current will this toaster use when connected to a 110 V power source?
Explanation / Answer
1.
1 feet =0.3048 m
Length L=20*0.3048 =6.096 m
1 Inch =0.0254 m
diameter d=0.0254*0.0285 =7.24*10-4 m
Surface Area
A=pi*d*L =pi*(7.24*10-4)*6.096=0.01386 m2
Radiant heat transfer from the wire is
P=e*A*sigma*T4
for black body e=1
P=1*0.01386*(5.67*10-8)*(750+273)4
P=861 Watts
b)
Current flowing through toaster is
P=VI
I=P/V =861/110
I=7.826 A