A car of the future requires 15kW of power to travel along a level road at 65km/h. A physics student wishes to use the car to dr
ive from Bowser to Qualicum, a distance of about 25 km. The engine is driven by heat energy recovered from a special material which has a specific heat capacity of 9800 J/kg • degree Celsius, If the car has 350 kg of this material, the outside air temperature is 15 °c and the engine is 88% efficient, to what temperature must the material be heated?
Power = Energy / time, The time is the one it takes to cover 25 km at 65 km/h, so: time = 25/65*60*60 = 1384.6 seconds.
Now the total energy needed for that is: Energy = Power * time = 15,000 * 1384.6 = 20769239.8 J.
The heat provides those J. The heat for a difference in temperature is:
Heat = mass * c_h * Difference_of_temperature,
Heat = 350 * 9,800 * (T-15)*0.88,
where the 0.88 is because some of the heat is lost, efficiency 88%. Now, you can equal both results and get T:
350*9,800*0.88*(T-15) = 20769239.8
T-15 = 6.88, and T = 21.88 C
The answer is T= 21.88 C
NB: this specific heat, 9,800, is more than 2,000 time sthat of water, it is really a substance that does not exist,. It seems He has the highest (5,300) but it's a gas!
