4.1.3: Problems
- Page ID
- 32761
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Exercise \(\PageIndex{1}\): Work and heat
As the \(100\text{-kg}\) red mass drops, a paddle turns in a liquid and the liquid heats up (position is given in meters and time is given in seconds). The dimension of the container that holds the liquid that you cannot see (into the screen) is \(0.1\text{ m}\). The density of the liquid is \(920\text{ kg/m}^{3}\). Restart. What is the heat capacity of the liquid in the animation?
Joule used a version of this device to determine the equivalence between heat and work.
Problem authored by Anne J. Cox.
Script authored by Anne J. Cox and Mario Belloni.
Exercise \(\PageIndex{2}\): Heating of a block stuck on a conveyor belt
The red block gets stuck on a conveyor belt (position is given in meters and time is given in seconds). Assume (rather unrealistically) that only the block heats up (and not the conveyor belt). Restart. If the \(4.3\text{-kg}\) red block is aluminum (specific heat of \(236\text{ J/kg}\cdot\text{K}\)) and the thermometer shows the temperature of the block, what is the coefficient of friction between the block and the conveyor belt?
Problem authored by Anne J. Cox.
Script authored by Anne J. Cox and Mario Belloni.
Exercise \(\PageIndex{3}\): Linear expansion
A rod is resting on a surface (you see the top view) and is attached to the surface at its middle (position is given in meters and time is given in minutes). The animation shows you both the rod and a magnified view of the right end. Restart. What is the coefficient of linear expansion of the rod?
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{4}\): Thermal expansion of a plate
The animation shows a close-up of the bottom-left corner of the square opening in a sheet of material (position is given in millimeters and time is given in minutes).
Figure \(\PageIndex{1}\)
The initial temperature is \(300\text{ K}\), which changes (increases or decreases) by \(200\text{ K}\) over the time of the animation (\(t = 2\) minutes). The opening is initially a \(20\text{ cm}\times 20\text{ cm}\) square. Restart.
- Determine if the temperature is increasing or decreasing.
- Find the coefficient of linear expansion.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{5}\): Fitting a plate over a ball-bearing
A plate with a hole in the middle needs to fit around a ball bearing. In the animation, you are looking at a side view of the plate and ball bearing shown below:
Figure \(\PageIndex{2}\)
The solid blue lines in the animation are the plate on either side of the bearing, and the dotted blue lines represent the part of the plate going over the ball bearing, which sticks out of the screen. Initially, the plate almost fits around the bearing, but to get it to fit around the middle of the ball, the blue plate and gray ball bearing are heated so that the temperature of the plate changes as indicated (position is given in millimeters). The coefficient of expansion of the ball bearing is much smaller than the plate so that you can neglect the expansion of the ball bearing in comparison with the plate.
Determine the coefficient of linear expansion of the plate. Restart.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{6}\): Specific heat and latent heat of fusion
This animation shows a container holding \(1\text{ kg}\) of a solid heated by a heater delivering \(2400\) watts to the material (temperature is given in kelvin and time is given in seconds). Restart. Find the specific heat capacity of the material and its latent heat of fusion. Ignore the heat capacity of the container.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{7}\): Calorimetry: ranking task
Run the animations and rank the materials in order of their specific heat capacity from smallest to largest (temperature is given in kelvin and time is given in arbitrary units). Restart. In each animation the same mass of material starts at the same temperature and is put into a thermally insulated container of water. The graph shows the temperature of the water and the material as a function of time.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{8}\): Calorimetry: find the specific heat
This animation shows a container holding \(1\text{ kg}\) of a solid heated by a heater delivering \(2400\) watts to the material (temperature is given in kelvin and time is given in seconds). Restart. Find the specific heat capacity of the material and its latent heat of fusion. Ignore the heat capacity of the container.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{9}\): Conductivity comparison
Move the slider to change the temperature on either side of the interface (position is given in centimeters and temperature is given in kelvin). Restart. Determine which of the two materials has a higher thermal conductivity.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{10}\): Window: single pane versus double pane
This animation represents a double-pane window with gas between the two panes of glass. Restart. Adjust the outside temperature and calculate the ratio of the conductivity of the glass and the conductivity of the gas inside the window (position is given in centimeters and temperature is given in kelvin). Compare (quantitatively) the heat per area conducted across the double-pane window with a window of the same total thickness made completely of glass (of the same conductivity as the glass in this problem).
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{11}\): Water heater insulation
Determine the conductivity of the \(10\text{-cm}\) thick insulation around the red water heater shown (this is a cross section of a cylindrical water heater). Restart. Assume that all the power from the heater at the bottom of the water heater is delivered to the water to keep it at the same temperature (\(50^{\circ}\text{C}\) in this case). Adjust the room temperature to see the change in power required from the heater (position is given in meters and temperature is given in degrees Celsius).
Problem authored by Anne J. Cox.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.