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)