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

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.

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### 1 Answer

Firs you need to find how much heat you create by burning a volume of gasoline

`V = 5.5 galons =3.785*5.5 =20.8175 Liter`

The density of gasoline is `rho =0.72 (kg)/L` so that its total mass is

`m = rho*V =20.8175*0.72 =14.99 =15 kg`

The energy content of gasoline is 42.4 MJ/kg. The heat generated by burning 15 kg of gasoline is

`Q =15*42.4*10^6 =6.36*10^8 =636 MJ`

All this heat need to be removed by the coolant.

`Q =m*c*(T_f-T_i)`

`m =Q/(c*(T_f-T_i)) =(6.36*10^8)/(3*(93-25))=3.11*10^6 grams =3117 kg`

In a car the mass of coolant is only a a few kg and still the car is running. This happens because the coolant is continuously circulated through the radiator where it is cooled and then through the engine where it is heated.

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