Q1A. What gauge pressure must you generate in your mouth to draw water up a 10 cm straw?

Background

Topic: Fluid Statics (Hydrostatics)

This question tests your understanding of pressure differences required to move fluids against gravity, specifically using the concept of gauge pressure and the hydrostatic pressure equation.

Key Terms and Formulas

• Gauge Pressure: The pressure relative to atmospheric pressure.

• Hydrostatic Pressure:

• = density of fluid (water: )

• = acceleration due to gravity ()

• = height of fluid column (convert cm to m!)

Step-by-Step Guidance

1. Identify the height of the water column: .

2. Recall that to draw water up, the pressure in your mouth must be lower than atmospheric pressure by the amount needed to support the water column.

3. Use the hydrostatic pressure formula: to calculate the pressure difference required.

4. Remember, gauge pressure is the difference from atmospheric pressure, so it will be negative (suction).

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Q1B. How many moles of helium are in a 1 m radius spherical balloon at STP, and what is the buoyant force?

Background

Topic: Ideal Gas Law and Buoyancy

This question tests your ability to apply the ideal gas law to find the number of moles in a gas-filled balloon and to calculate the buoyant force using Archimedes' principle.

Key Terms and Formulas

• Volume of a sphere:

• Ideal Gas Law:

• Buoyant Force:

• Standard Temperature: , Standard Pressure:

• Gas constant:

Step-by-Step Guidance

1. Calculate the volume of the balloon using .

2. Use the ideal gas law to solve for (number of moles): .

3. Calculate the buoyant force using the air density, the volume of the balloon, and .

4. Make sure all units are consistent (SI units).

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Q1C. Sketch and compare isobaric, isothermal, and adiabatic expansions on a PV diagram. Rank the heat transferred (Q) for each process.

Background

Topic: Thermodynamics—Gas Processes

This question tests your understanding of different thermodynamic processes (isobaric, isothermal, adiabatic) and how heat transfer differs among them for the same initial and final volumes.

Key Terms and Formulas

• Isobaric: Constant pressure

• Isothermal: Constant temperature

• Adiabatic: No heat exchange ()

• First Law of Thermodynamics:

• For monoatomic ideal gas: ,

Step-by-Step Guidance

1. Sketch the three processes on a PV diagram, all starting at and ending at .

2. Recall that for isobaric, pressure is constant; for isothermal, is constant; for adiabatic, is constant ().

3. Consider the heat transferred in each process using the first law and the specific heat values.

4. Rank the heat transferred () for each process based on your analysis.

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Q1D. Rank the work done by the gas in each expansion (isobaric, isothermal, adiabatic).

Background

Topic: Thermodynamics—Work in Gas Processes

This question tests your understanding of how to calculate and compare the work done by a gas during different types of expansions, using graphical and analytical reasoning.

Key Terms and Formulas

• Work done by gas:

• Isobaric:

• Isothermal:

• Adiabatic:

Step-by-Step Guidance

1. Recall the work formulas for each process.

2. Compare the area under each curve on the PV diagram (work is the area under the curve).

3. Rank the work done for each process based on the formulas and/or graphical reasoning.

4. Justify your ranking using the properties of each process.

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Q1E. What is the most probable speed in the 2D Maxwell distribution of speeds?

Background

Topic: Statistical Mechanics—Maxwell Speed Distribution

This question tests your ability to analyze a probability distribution and find the most probable value (mode) for particle speeds in two dimensions.

Key Terms and Formulas

• 2D Maxwell Distribution:

• Most probable speed: Value of where is maximized

• Set to find the maximum

Step-by-Step Guidance

1. Write the given 2D Maxwell distribution function.

2. Take the derivative with respect to and set it equal to zero to find the maximum.

3. Solve the resulting equation for to find the most probable speed.

4. Simplify your answer in terms of , , and .

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Q2A. Given a snapshot of a traveling wave at , determine and sketch at s.

Background

Topic: Waves—Traveling Waves

This question tests your ability to interpret a wave snapshot, write the wave function, and predict its future shape given its velocity and direction.

Key Terms and Formulas

• Traveling wave: (for rightward motion)

• Wave velocity:

• Snapshot at gives

Step-by-Step Guidance

1. Analyze the given graph to determine amplitude, wavelength, and phase.

2. Write the general form of the wave function for rightward motion.

3. Use the given velocity to relate and .

4. Sketch the wave at s by shifting the wave to the right by .

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Q2B. For a standing wave in a 0.9 m tube, write and determine if the tube is open or closed at the ends.

Background

Topic: Standing Waves—Boundary Conditions

This question tests your understanding of standing wave patterns, their mathematical description, and how boundary conditions (open/closed ends) affect the wave.

Key Terms and Formulas

• Standing wave: (for nodes at both ends)

• Boundary conditions: Open end = antinode, closed end = node

• Tube length relates to wavelength: (open-open), (open-closed)

Step-by-Step Guidance

1. Examine the graph to identify nodes and antinodes at the tube ends.

2. Write the general form of the standing wave function based on the observed pattern.

3. Use the tube length and pattern to determine if the tube is open or closed at the ends.

4. Justify your answer using the relationship between tube length and wavelength for each case.

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