Physics 202 Homework, Day 02: Chapter 11 : 1, 16, 22, 25, 34
ü 1. The highest recorded waterfall in the world is Angel Falls in Venezuela. Its longest single waterfall has a
height of 807 m. If the water at the top is 15.0 °C, what is the maximum possible temperature of the water at
the bottom of the falls? Assume all the kinetic energy of the water as it reaches the bottom goes into
raising the water's temperature. (This is not realistic, but it gives us a number to check against an
experimental value.)
The mass of water cancels out in this problem: m g h = m c DT => DT =
In[21]:=
gh
c
g = 9.8; h = 807.; cWater = 4186.; TInitial = 15.0;
gh
DT =
;
cWater
Print@"Temperature change is ", DT,
"°C, and the final temperature is ", TInitial + DT, " °C."D
Temperature change is 1.8893°C, and the final temperature is 16.8893 °C.
ü 16. Lead pellets, each of mass 1.00 g are heated to 200 °C. How many pellets must be added to 500 g of
water, initially at 20.0 °C to make the final equilibrium temperature 25.0 °C? Neglect any energy transfer to
or from the container. The specific heat of lead is 128 J/kg °C.
Heat gained by lead + Heat gained by water = 0 (Heat is lost by the lead and gained by the water.)
(pellets*mass of each pellet)*cLead*(TFinal-TInitialLead) + (mass of water)*cWater*(TFinal-TWaterInital) = 0
=> (pellets*mass of each pellet)*cLead*(TFinal-TInitialLead) = - (mass of water)*cWater*(TFinal-TWaterInital)
Hmass of waterL*cWater*HTFinal-TWaterInitalL
mass of each pelletL*cLead*HTFinal-TInitialLeadL
=> pellets = In[27]:=
mWater = .500; mLead = .001 * Pellets; cLead = 128.; cWater = 4186.; TFinal = 25.0;
TWaterInitial = 20.0; TLeadInitial = 200.; H* values for this problem *L
pellets = - HmWater * cWater * HTFinal - TWaterInitialLL ê H.001 * cLead * HTFinal - TLeadInitialLL
Out[27]=
467.187
ü 22. When a driver brakes an automobile, the friction between the brake drums and the brake shoes
converts the car's kinetic energy to thermal energy. If a 1500 kg automobile travelling at 30 m/s is braked to
a halt, how much does the temperature rise in each of the four 8.0 kg iron brake drums? The specific heat
of iron is 448 J/kg °C.
The kinetic energy of the car is converted into heat energy which heats up the brake drums.
1
1
2
M v2 = 4 * m c DT => DT =
In[32]:=
2
M v2
4*m c
mCar = 1500.; vCar = 30.; mBrake = 8.0; cIron = 448.;
1
DT =
2
mCar * vCar2
4 mBrake * cIron
; Print@"The temperature will rise by ", DT, " °C."D
The temperature will rise by 47.0843 °C.
2
Day_02_sol.nb
ü 25. A 75-g ice cube at 0 °C is placed into 825 g of water at 25 °C. What is the final temperature of the
mixture? (Remember to include the latent heat of melting for the ice cube...)
Remember that the energy must be supplied to melt the ice before its temperature will begin to rise.
Qice + Qwater = 0 =>
mIce*Lf + mIce*c*(Tfinal-0) + mWater*c*(TFinal-25)
=>
mIce*c*Tfinal
+
mWater*c*(TFinal)
=
mWater*c*(25)
mIce*Lf
=> Tfinal =
In[35]:=
mWater*c*H25L-mIce*Lf
HmIce+mWaterL*c
mWater = 825.; mIce = 75.; TWaterInitial = 25.; cWater = 4186.;
mWater * cWater * TWaterInitial - mIce * Lf
Lf = 333 000.; TFinal =
;
HmIce + mWaterL * cWater
Print@"The final temperature is ", TFinal, " °C"D
The final temperature is 16.2874 °C
ü 34. A 60.0 kg runner expends 300 Watts of power while running a marathon. Assuming 10% of the energy
is delivered to the muscle tissue to do useful work and that the excess energy is removed from the body
by sweating and evaporation to keep the runner's temperature constant, determine the volume of bodily
fluid (assume is water) lost per hour. The latent heat of vaporization of water (at body temperature) is
2.41*106 J/kg.
In[8]:=
HeatPerSecond = 300. * .90; LatentHeat = 2.41 * 106 ;
WaterMass = HHeatPerSecond * 60 * 60L ê LatentHeat;
Print@"The amount of water lost per hour is ", WaterMass, " kg."D
The amount of water lost per hour is 0.40332 kg.
In[11]:=
WaterVolume = WaterMass * 1 ; H* 1 Literêkilogram *L
Print@"The volume of water lost per hour is ", WaterVolume, " liters."D
The volume of water lost per hour is 0.40332 liters.