4. A typical car engine produces 44,000 kJ of heat in an hour. The cooling system has a capacity of 8.40 L and is filled with a 50:50 mixture of anti-freeze (specific heat capacity of 8.37 J/g-oC, density of 1.038 g/mL). In maintaining a constant engine temperature, the cooling system temperature increased from 95oC to 110oC. (Assume this is within allowable limits.) How many times did the cooling system turn over its volume of anti-freeze to maintain the engine temperature during its hour of operation? Show your work. (Assume that only the cooling system removes heat from the engine and no other mechanism of heat removal is involved.)
My work so far:
First calculate mass of the coolant
8.7912 = 8.4 * 1.038.
Energy absorbed by coolant is
1,103.73516 = 8.7912 * 8.37 * 15
I can't figure out what to do next.
I wouldn't tackled it this way, and you are free to not use what I am telling you because I can not be 100% positive about the answer. However, I would go this route:
q=44,000 kJ=4.4 x 10^4 kJ=4.4 x 10^7 J
t=110 C-95 C=15 C
Solve for m:
m=(4.4 x 10^7 J)/[(8.37 J/g*C)(15 C)
You know m (mass in g), use the density to solve for the volume:
Convert mL to L:
1mL= 10^-3 L
Take the total volume, which I believe will be bigger, than the volume of the container, and solve for the number of cycles:
Volume that you solved for using the density and converted to L:
Volume in L/8.40L
***Answer with 3-significant figures.
posted by Devron