1.(10 points, suggested time 20 minutes)
A sample of ideal gas is taken through the thermodynamic cycle shown above. Process C is isothermal.
(a)Consider the portion of the cycle that takes the gas from state 1 to state 3 by processes A and B. Calculatethe magnitude of the following and indicate the sign of any nonzero quantities.
- The net change in internal energy △U of the gas
- The net work W done on the gas
- The net energy Q transferred to the gas by heating
(b) Consider isothermal process C.
i. Compare the magnitude and sign of the work W done on the gas in process C to the magnitude and sign of the work in the portion of the cycle in part (a). Support your answer using features of the graph.
ii. Explain how the microscopic behavior of the gas particles and changes in the size of the container affect interactions on the microscopic level and produce the observed pressure difference between the beginning and end of process C.
(c) Consider two samples of the gas, each with the same number of gas particles. Sample 2 is in state 2 shown in the graph, and sample 3 is in state 3 shown in the graph. The samples are put into thermal contact, as shown above. Indicate the direction, if any, of energy transfer between the samples. Support your answer using macroscopic thermodynamic principles.
2. (12 points, suggested time 25 minutes)
A group of students design an experiment to investigate the relationship between the density and pressure of a sample of gas at a constant temperature. The gas may or may not be ideal. They will create a graph of density as a function of pressure. They have the following materials and equipment.
- A sample of the gas of known mass Mg in a sealed, clear, cylindrical container, as shown above, with a movable piston of known mass mp
- A collection of objects each of known mass mo
- A meterstick
i. Describe the measurements the students should take and a procedure they could use to collect the data needed to create the graph. Specifically indicate how the students could keep the temperature constant. Include enough detail that another student could follow the procedure and obtain similar data.
ii. Determine an expression for the absolute pressure of the gas in terms of measured quantities, given quantities, and physical constants, as appropriate. Define any symbols used that are not already defined.
iii. Determine an expression for the density of the gas in terms of measured quantities, given quantities, and physical constants, as appropriate. Define any symbols used that are not already defined.
iv. The graph above represents the students’ data. Does the data indicate that the gas is ideal?Describe the application of physics principles in an analysis of the graph that can be used to arrive at your answer.
Another group of students propose that the relationship between density and pressure could also be obtained by filling a balloon with the gas and submerging it to increasing depths in a deep pool of water.
(b) Why could submerging the balloon to increasing depths be useful for determining the relationship between the density and pressure of the gas?
(c) The balloon is kept underwater in the deep pool by a student pushing down on the balloon, as shown above.Let Vb represent the volume of the inflated balloon, mb represent the mass of just the balloon (not including the mass of the gas), Pg represent the density of the gas in the balloon, and Pw represent the density of the water.Derive an expression for the force the student must exert to hold the balloon at rest under the water, in terms of the quantities given in this part and physical constants, as appropriate.