Question 1

A diver slowly lowers a block into the ocean. Given several pictures showing the block at different depths, which graph best represents the buoyancy force acting on the block as a function of time?

Accepted Answer

The buoyancy force increases as the block is lowered deeper, then levels off when fully submerged.

Question 2

Which of the following best describes the relationship between temperature and pressure for a fixed amount of gas at constant volume, according to the ideal gas law?

Accepted Answer

Pressure is directly proportional to temperature.

Question 3

A sealed container holds air at room temperature. If the temperature is doubled while keeping the volume constant, what happens to the average kinetic energy of the air molecules?

Accepted Answer

It is doubled.

Question 4

Which equation correctly expresses the change in pressure with height in the atmosphere, assuming constant temperature?

Accepted Answer

$$P = P_0$ e$$^{-\frac{gh}$${RT}}$$

Question 5

A metal rod is heated at one end. Which of the following best describes the direction of heat flow and the change in temperature along the rod over time?

Accepted Answer

Heat flows from the hot end to the cold end, and temperature decreases along the rod.

Question 6

Which of the following is the correct formula for the root mean square (rms) speed of a molecule in an ideal gas?

Accepted Answer

$$v_{rms} = \sqrt{\frac{3kT}{m}}$$

Question 7

A gas is compressed in a piston at constant temperature. What happens to the entropy of the gas?

Accepted Answer

Entropy decreases.

Question 8

Which of the following best describes the change in internal energy for an ideal gas during an isothermal expansion?

Accepted Answer

Internal energy remains constant.

Question 9

A steam engine operates between a boiler at $$T_H = 500 \ \mathrm{K}$$ and a condenser at $$T_C = 300 \ \mathrm{K}. $$What is the maximum possible efficiency of this engine?

Accepted Answer

$$\eta = 1 - \frac{T_C}{T_H} = 0.4$$

Question 10

Which of the following statements about entropy is correct?

Accepted Answer

Entropy is a measure of disorder or randomness in a system.

Question 11

A container is divided into two compartments by a removable partition. One side contains gas A, the other side contains gas B. When the partition is removed, what happens to the entropy of the system?

Accepted Answer

Entropy increases because the gases mix.

Question 12

Which of the following is the correct expression for the change in entropy $$\Delta S$$ when $$Q$$ amount of heat is added reversibly to a system at temperature $$T$$?

Accepted Answer

$$\Delta S = \frac{Q}{T}$$

Question 13

A sample of gas undergoes an adiabatic expansion. Which of the following statements is true?

Accepted Answer

The temperature of the gas decreases.

Question 14

Which of the following is the correct formula for the number of moles $$n in a $$sample, given mass $$m$$ and molar mass $$M$$?

Accepted Answer

$$n = \frac{m}{M}$$

Question 15

A gas is contained in a cylinder with a movable piston. If the pressure is kept constant and the temperature is increased, what happens to the volume?

Accepted Answer

Volume increases.

Question 16

Which of the following is the correct expression for the work done by an ideal gas during an isothermal expansion from volume $$V_i to$$ $$V_f at $$temperature $$T$$?

Accepted Answer

$$W = nRT \ln \left( \frac{V_f}{V_i} \right)$$

Question 17

Which of the following best describes the change in volume of a gas when the pressure is doubled at constant temperature?

Accepted Answer

Volume is halved.

Question 18

A wave is shown in a picture. Which of the following quantities can be determined directly from the image?

Accepted Answer

Wavelength and amplitude.

Question 19

Which of the following is the correct formula for the pressure exerted by an ideal gas in terms of molecular speed?

Accepted Answer

$$P = \frac{1}{3} n m v_{rms}^2$$

Fluid Mechanics, Buoyancy, and Thermodynamics: Study Notes

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