Acar 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 drive 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!