Heat Energy Calculations

 

1.     What is the change in energy ÆEh of a beaker containing 0.050 kg of water if its temperature increases from 15o to 26o Celsius? ÆEh = mcÆT = 2310 J

2.     250,000 J of heat energy is given to a pan containing 1.8 kg of water. 

a)   What will be its increase in temperature (ÆT)? ÆT = ÆE/mc = 33ûC

b)   What will be its final temperature if it started at 22ûC? 33 + 22=55ûC

3.     0.057 kg of aluminum at 95o C is added to 0.080 kg of water at 16o C. What will be the temperature of the 0.137 kg of water after total mixing? (heat capacity  (aluminum) = 900 J/kgûC 26.5ûC

4.     A motorcycle racer (total mass = 670 kg) slows from 97 m/s to 28 m/s in 6.4 s.

a)   What is the loss in his kinetic energy? 2 890 000 J

b)   What is the power loss during this time? 451 400 W or 451 kW

c)   How many 100 W light bulbs could be lit during the 6.4 seconds? 100 W = 100 J/s for one light bulb so one light bulb uses 640 J in 6.4 s. If the total energy is 2 890 000 J then 2 890 000 J/640 J = 4516 light bulbs.

d)   If the heat produced in the brake linings were used to heat up 8 kg (8 litres) of water in a radiator, what would be the change in temperature of the water during braking?                                                      ÆEh = mcÆT, ÆT=ÆEh/mc = 86ûC

5.     120,000 kg of water drops 280 m from a dam each minute.

a)   What is the change in Potential Energy of the water?                                                            Use Ep =mgh = (120 000 kg)(9.80 m/s2)(280 m) = 329.3 MJ per minute (329 300 000 J or 3.293 x 1010 J)  note that this is É 5 488 000 J/s

b)   If the power station is 80% efficient what is the amount of electrical energy that can be produced in one hour? 329.3 MJ per minute converts to 19 760 MJ per hour but the process is only 80% efficient so (0.80)(19760 MJ)= 15 806 MJ per one hour

c)   i) What is the POWER output (in Watts) of this power station? (Note W = J/s) P=ÆE/t = 15 806 000 000 J/h = 4 390 000 W

      ii) in Kilowatts 4390 kW

d)   If electrical water heaters in homes are 95% efficient, how many kilograms of water could be heated from 18ûC to 33ûC for baths in one hour given the electrical energy supplied by the power plant? m=E/cÆT=(.95)(4 390 000 J/s)(3600 s)/(4200 J/kgûC x 15ûC) = 238 300 kg

      How many kilograms of water are there in one bathtub of water? (Estimate!) 100 L therefore 100 kg

      How many baths could be filled with hot water in one hour from this power station? 238 300 kg/100 kg = 2380 baths

e)   How many 100 W light bulbs could be lit continuously by this power station? 100 W = 100 J/s, plant produces 4 390 000 J/s therefore 43 900 bulbs could be lit continuously.

f)   If a B.C. Hydro bus full of passengers has a mass of 12,000 kg how many bus loads could be lifted up to a height of 130 m with one hourÕs worth of electricity from this power station? W=ÆE          Wlift bus = mgh = (12 000 kg)(9.80 m/s2)(130 m) = 15 288 000 J. The power plant produces 1.58 x 1010 J in one hour (4 390 000 J/s x 3600s). Therefore, 1033 buses could be lifted (1.58 x 1010 J/15 288 000 J)