🧲AP Physics 2
3. In Experiment 1, a student is given a rigid, thermally insulated container of unknown internal volume V containing a sample of dry air that can be treated as an ideal gas. The container is fitted with a digital pressure sensor and a temperature probe that measure the pressure P and temperature T of the gas inside. The student is asked to design an experiment to determine the container volume V and to relate the measured pressure and temperature to the microscopic model of gases.
Describe a procedure for collecting data that would allow the student to determine the internal volume V of the container. In your description, include the measurements to be made. Include any steps necessary to reduce experimental uncertainty.
Describe how the collected data could be analyzed to determine V. Include references to appropriate equations and to relationships between measured and known quantities. Your description should connect the measured macroscopic variables to a microscopic model of temperature and pressure in an ideal gas.
Figure 1. Rigid, thermally insulated container with dry-air inlet, valve, digital pressure sensor, and temperature probe; container shown in three possible thermal environments (273 K ice bath, 293 K water bath, 353 K hot-water bath).
Figure 2. Blank grid for plotting a straight-line graph to determine container volume V (example axes set for P versus T).
T (K) | P (kPa) |
|---|---|
273 | 93.2 |
293 | 100.0 |
313 | 106.8 |
333 | 113.8 |
353 | 120.8 |
In Experiment 2, the student seals a fixed amount of dry air in the container and places the container in water baths of different temperatures. After thermal equilibrium is reached in each bath, the student records the gas temperature T and pressure P. The data are shown in Table 1.
Indicate two quantities, either measured quantities from Table 1 or additional calculated quantities, that could be graphed to produce a straight line that could be used to determine the container volume V.
Vertical axis: Horizontal axis:
On Figure 2, create a graph of the quantities indicated in part C(i) that can be used to determine V.
Use Table 2 to record the data points or calculated quantities that you will plot.
Clearly label the axes, including units as appropriate.
Plot the points you recorded in Table 2.
Draw a best-fit line for the data graphed in part C(ii).
Using the best-fit line that you drew in part C(iii), calculate an experimental value for the container volume V. In Experiment 2, before collecting the data in Table 1 the student measured the mass of dry air sealed in the container to be . Use the best-fit line from part C(iii) to determine the container volume. Treat air as an ideal gas with molar mass and . (Note: .)
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