Question

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.)

Answer 1

To find the 'number of times' the cooling system was operated, I believe you'll need to find \(\frac{∆H_{surr}}{q_{sys}}\)

It is given that \(∆H_{surr}=44,000 kJ\)
To find \(q_{sys}\), you must use the formula for q:
\(q=mc∆T\)
Here,
\(•m=8.40\ L\ \cdot\frac{1000\ mL}{1\ L}\cdot\frac{1.038\ g}{1\ mL}\)
=\(8,719.2≈8,719~g~\text{antifreeze}\) to the significant figure.
\(•c_s=8.37~J/g°C\)
\(•∆T=T_f-T_i=110°C-95°C=15°C\)
Substitute the values

\(q_{sys}=(8719~g)(8.37~J/g°C)(15°C)=1.095 \times 10^6 J\)
\(≈1.095 \times 10^3 kJ\)

That is your \(q_{sys}\). But this is not your final answer.

\(\frac{∆H_{surr}}{q_{sys}}=\frac{44,000~kJ}{1095~kJ}=\rule{1cm}{0.15mm}\)
Fill in the blank (evaluate that using a calculator)