If your coolant starts out at 25 °C, how many kilograms of coolant would you need to keep your vehicle running after burning 5.5 gallons of gasoline?A 70/30 mixture of antifreeze/water gives a...

If your coolant starts out at 25 °C, how many kilograms of coolant would you need to keep your vehicle running after burning 5.5 gallons of gasoline?

A 70/30 mixture of antifreeze/water gives a much better range of -55 °C to 113 °C, but has a lower specific heat of about 3.00 J/(g x °C). Your engine works well when the coolant temperature is near 93 °C. If your coolant starts out at 25 °C, how many kilograms of coolant would you need to keep your vehicle running well after burning those 5.5 gallons of gasoline while driving (final temperature of coolant is 93 °C)? Show your work including any necessary formulas, all conversions, and all units.

bandmanjoe | Middle School Teacher | (Level 2) Senior Educator

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Gasoline is the most prevalent fuel used to power automobiles and trucks world wide.  It has octane, which is a hydrocarbon with eight carbon atoms in its principal chain.  Gasoline provides 132 megaJoules of heat energy when combusted with oxygen per United States gallon.

For starters, lets convert the 5.5 gallons to total energy output:

132 MJ/gal. x 5.5 gal. = 726 MJ Total energy.

The formula for calculating specific heat capacity problems is Q = cm^T, where Q is the total heat energy, c is the specific heat capacity, m is the mass of the substance, and ^T is the change in temperature.  So, if we substitute the numbers we have available, the equation should look like this:

726 MJ = (.000003 MJ/g x C)(mass)(68 degrees Celsius)

I converted the 3 J/g x C by dividing it by 1,000,000 joules per MJ.

The change in temperature was 93 - 25 = 68 C.

So, proceeding with the math, we get 726 MJ = .000204 MJ/g x C(mass).  If we divide both sides by the .000204, we get 3,558,823.5 grams = mass.  To convert that to kilograms, divide by 1000, since there are 1000 grams per kilogram.  That gives us an answer of 3558.8 kg of coolant needed to maintain the motor at  93 degrees Celsius.

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