Lab 34: Coming to a boil ; Sharing energy I ; Sharing energy II:
heat capacity of aluminum
- Relation between thermal energy and temperature
- Effect of heat energy in a material
- Heat capacity and different materials
9) You are given 3 samples of water, as follows:
#1: 100 cm3 of water at 80°C
#2: 50 cm3 of water at 40°C
#3: 150 cm3 of water at 10°C
If all 3 of these are mixed together (before heat can be lost to the surroundings), what is
the final temperature of the water?
Let’s mix #1 and #2 first. There is twice as much water at 80° as at 40°, so
you average them, but count the 80° water twice: (40 + 80 + 80)/3 = 66.6°.
Then mix this 150 cm3 water with the 150 cm3 of 10° water (#3) - these are
equal amounts, so you just average the temperature: (66.6 + 10)/2 = 38.3°
The final temperature is 38.3°C.
10) Aluminum has a heat capacity of about 900 Joules/kg/°C, while water has a heat
capacity of about 4000 Joules/kg/°C. 100 g of aluminum in thermal equilibrium is taken
from a pot of boiling water and dropped into 1000 cm3 of pure water (no ice) at 0°C.
a) What is the initial temperature of the aluminum? 100°C
b) When the aluminum is dropped into the 1000 cm3 of pure water, from which material
to which material does thermal energy flow?
Thermal energy flows from from the higher temperature aluminum to the
lower temperature water.
c) At what point does thermal energy stop flowing?
Thermal energy stops flowing when the aluminum temperature drops and
water temperature raises to the point of thermal equilibrium, and they are
both the same temperature.
d) According to the Law of Conservation of Energy, how does the thermal energy lost by
the aluminum compare to the thermal energy gained by the water? (Assume the
container is well-insulated, so no heat can transfer to or from the surroundings.)
If energy is conserved, then it is not created or destroyed - so the thermal
energy lost by the aluminum must equal the thermal energy gained by the
water.
e) After a long amount of time, how do the temperatures of the 100 g of aluminum and
1000 cm3 of water compare?
As stated in c), the temperatures will eventually be equal, when they reach
thermal equilibrium.
f) Using what you know about heat capacity and how it relates to thermal energy, is it
possible to find the final temperature of the aluminum+water in the end?
Note: You don’t have to solve this problem (though you can give it a try if you want) just try to explain how someone would start setting this problem up....
This CAN be done: you would set the energy lost by the aluminum equal to
the energy gained by the water:
energy lost by aluminum = energy gained by water
–mass of Al. × heat capacity of Al. × change in temp. of Al.
= mass of H2O × heat capacity of H2O × change in temp. of H2O
Knowing that change in temp. = initial temp – final temp, and knowing the
final temperatures are equal, you could then algebraically solve for the final
temperature.
Lab 35: How Long Does Your Coffee Stay Hot?
- Effect of insulators and conductors on heat energy
- Heat, energy and power
- Heat capacity and storage of thermal energy
11) Kristin wants to design a picnic carrier divided into 2 halves - one for hot foods, and
the other for cold foods. She researches several different materials, and considers how
different materials “feel” upon touching.
a) Kristin thinks metal would good for building the cold half of the carrier, because metal
seems “cold” when she touches it. Is Kristin correct? Explain.
No - metal is a conductor, not an insulator; it would actually make her cold
side reach thermal equilibrium faster, which would not be desired.
b) Kristin notes that wool feels warm in clothing - so she thinks that a wool-like
insulation would work better for insulating the cold half of the cooler than the warm half.
Is Kristin correct? Explain.
No - wool is a decent insulator (and might be a good material), but it
wouldn’t work any better for one half than the other, based on her
reasoning - a good insulator will keep heat out as well as keep heat in.
c) To keep the picnic carrier at the correct temperatures, which part of the carrier would
require the most insulation, and why?
The center separating the 2 halves would need to be best insulated, since
the hot and cold sides are further from thermal equilibrium than either side
is from the surroundings, and would be prone to transfer thermal energy
through the center barrier the most quickly.
d) Kristin has the idea of making 2 packets of a material to insert on either side to keep
the hot side hot and the cold side cold, by cooling one packet in the freezer and heating
the other in the oven before use. What properties should she look for in a material that
can best do this job?
Above all, Kristin would want her packets to made of a material of a high
heat capacity, so it could absorb the most thermal energy on the cold side,
and release the most thermal energy on the hot side.
12) A typical microwave oven uses 1000 Watts. Using some reasonable estimated
values of volume, heat capacity, and temperature, determine how much time, at
maximum power, it takes to heat up a cup of hot cocoa or coffee to drink. Does the
value you find match common experience?
Volume of a 12 oz cup is about 0.35 liters. 1 liter of water is 1 kg, so 0.35 kg
is a good value for the drink’s mass.
Heat capacity of water is about 4000 J/kg/°C.
We start at room temperature (about 20°C) and want to get it hot but not
boiling (about 70°C), so the change in temperature is about 50°C.
Thermal energy = mass × heat capacity × change in temperature
= 0.35 kg × 4000 J/kg/°C × 50°C = 70000 J
1 watt = 1 J/sec, so
70000 J / 1000 J/sec = 70 seconds.
This is a perfectly reasonable amount of time to heat up a drink in a
microwave.
Lab 36: Melting Ice the Hard Way ; Another Way to Be Cool
- Phase changes and heat energy
- Temperature during a phase change
- Evaporation and heat energy
13) A cold beverage containing ice is left out on a countertop.
a) Assuming the ice and beverage are well mixed, what is its (approximate) initial
temperature?
If it contains ice and water, it will be about 0°C. (Things like sugar in the
drink might change this slightly, but not much....)
b) The ice begins to melt, and is completely melted by 30 minutes. Assuming again the
beverage stays well mixed, what happens to its temperature during this 30 minutes?
Thermal energy would go into melting the ice, so the temperature would
not change - it would still be 0°C.
c) Once the ice is all melted, what will happen to the temperature of the beverage?
Once the ice melts, the temperature will start to rise.
d) Make a plot of the approximate behavior of the temperature of the beverage over a
period of one hour below. (You will have to determine values for the vertical axis
yourself.)
The dotted line represents the equilibrium (room) temperature.
e) Is the rate at which thermal energy is transferred from the room to the cup in this plot
constant? If not, how does it change with time?
It is not quite constant, and is largest when the temperature is lower, that
is, at 0°C. The rate of energy transfer stays fairly constant, but starts to
decrease when it gets near room temperature.
f) You saw a physical example plotted in class where thermal energy was transferred at
a (close to) constant rate. What was this example, and what did the plot look like?
When water was heated in a kettle, the temperature increase appeared as a
straight line, meaning the rate at which thermal energy was added was
constant.
14) Both the evaporation and boiling of water are processes with similarities and
differences.
a) How are evaporation and boiling similar?
Both evaporation and boiling are a phase change from a liquid to a gas,
and both require the transfer of thermal energy.
b) How are evaporation and boiling different?
Boiling only happens at a high temperature (100°C), while evaporation can
happen at any temperature.
c) Think of what conditions are necessary to bring a substance (like water) to a boil.
How does thermal energy behave in this case? What happens to the temperature after
it begins to boil?
To boil water, thermal energy must be added to it - this added energy is
needed for the phase change from liquid to gas, so it doesn’t change
temperature while boiling.
d) Think of what conditions are necessary for a substance (like water) to evaporate.
From your observations, what does evaporation do to temperature? How does thermal
energy behave in this case?
Water can evaporate at any temperature - you just need dry (low-humidity)
air. Evaporation lowers temperature, because, like any phase change, it
requires a transfer of energy. In this case, the added thermal energy from
the environment cools it, and the energy goes into the phase change.