Q: A completely submerged chunk of metal sinks in water with an acceleration equal to one-fifth of $$g$$ ($$g = 9.8\ \mathrm{m/s^2$}). $$What is the density of the metal? Ignore all drag effects; only weight and buoyancy act on the chunk.

$$\rho_{\text{metal}} = 1.25\ \rho_{\text{water}}$$

Q: Water flows from a pipe with a speed of $$2.0\ \mathrm{m/s}$$ and a cross-sectional area of $$10\ \mathrm{cm^2$}$$ into the air. If the pipe is $$4.0\ \mathrm{m}$$ below the open surface, what is the water pressure as it exits into the air?

$$P = 3.92 \times 10^5$\ \mathrm{Pa}$$

Question 1

A completely submerged chunk of metal sinks in water with an acceleration equal to one-fifth of $$g$$ ($$g = 9.8\ \mathrm{m/s^2$}). $$What is the density of the metal? Ignore all drag effects; only weight and buoyancy act on the chunk.

Accepted Answer

$$ho_{	ext{metal}} = 1.25\ ho_{	ext{water}}$$

Question 2

In the figure, a vertical cylinder is filled with water and has a piston at the top. If the area of the piston is $$100\ \mathrm{cm^2$}$$ and the height of the water column is $$40\ \mathrm{cm}$$, what is the force exerted by the water on the piston?

Accepted Answer

$$F = 39.2\ \mathrm{N}$$

Question 3

Water flows from a pipe with a speed of $$2.0\ \mathrm{m/s}$$ and a cross-sectional area of $$10\ \mathrm{cm^2$}$$ into the air. If the pipe is $$4.0\ \mathrm{m}$$ below the open surface, what is the water pressure as it exits into the air?

Accepted Answer

$$P = 3.92 	imes 10^5$\ \mathrm{Pa}$$

Question 4

Air flows through a horizontal tube at a rate of $$1500\ \mathrm{cm^3$/s}. $$The tube has a constriction where the diameter narrows from $$4.0\ \mathrm{cm} to$$ $$2.0\ \mathrm{cm}. $$What is the height $$h of $$mercury in the right side of the U-tube manometer connected to the constriction?

Accepted Answer

$$h = 0.24\ \mathrm{m}$$

Question 5

A gas undergoes three processes: isothermal, isobaric, and adiabatic. Which process involves no heat transfer to or from the gas?

Accepted Answer

Adiabatic

Question 6

For a Carnot engine operating between $$T_H = 500\ \mathrm{K}$$ and $$T_C = 300\ \mathrm{K}$$, what is the maximum possible efficiency?

Accepted Answer

$$e = 0.60$$

Question 7

A refrigerator removes $$105\ \mathrm{J} of $$heat from the cold reservoir and does $$78\ \mathrm{J} of $$work. What is the coefficient of performance (COP) of the refrigerator?

Accepted Answer

$$	ext{COP} = 1.35$$

Question 8

A heat engine absorbs $$400\ \mathrm{J} of $$heat and does $$120\ \mathrm{J} of $$work. How much heat is expelled to the cold reservoir?

Accepted Answer

$$Q_C = 280\ \mathrm{J}$$

Question 9

Which of the following statements about the first law of thermodynamics is correct?

Accepted Answer

It states that the change in internal energy equals heat added to the system minus work done by the system: $$\Delta U = Q - W.$$

Question 10

A diatomic gas undergoes a cycle shown in a $$p$$-$$V$$ diagram. If the temperature at point 1 is $$20^\circ\mathrm{C}$$, and the process 1-2 is isobaric, what is the work done by the gas during this process?

Accepted Answer

$$W = p(V_2$ - V_1$)$$

Question 11

During an isothermal expansion of an ideal gas, which of the following is true?

Accepted Answer

The internal energy of the gas remains constant.

Question 12

In a $$p$$-$$V$$ diagram, which engine has the larger efficiency: Engine 1 (rectangular cycle) or Engine 2 (triangular cycle)?

Accepted Answer

Engine 2

Question 13

A gas expands adiabatically from $$V_1 to$$ $$V_2. $$Which equation correctly relates the initial and final temperatures and volumes for a monatomic ideal gas?

Accepted Answer

$$T_1$$ $$V_1$$^\gamma = $$T_2$$ $$V_2$$^\gamma$$

Question 14

A heat engine operates between $$T_H = 600\ \mathrm{K}$$ and $$T_C = 300\ \mathrm{K}$$, absorbing $$1200\ \mathrm{J} of $$heat from the hot reservoir. What is the maximum work output possible?

Accepted Answer

$$W = 600\ \mathrm{J}$$

Question 15

Which process on a $$p$$-$$V$$ diagram corresponds to a constant temperature?

Accepted Answer

Isothermal

Question 16

A gas is compressed isothermally. What happens to the entropy of the gas?

Accepted Answer

It decreases.

Question 17

A piston contains $$0.10$$ mol of nitrogen gas. During an isothermal expansion from $$V_1 = 1000$$\ \mathrm{$$cm^3$$}$$ to V_2$ = 2000\ \mathrm{cm^3$} at$$ $$T = 133^\circ\mathrm{C}$$, what is the work done by the gas?

Accepted Answer

$$W = nRT \ln \left( \frac{V_2$}{V_1$} \right)$$

Question 18

Which of the following best describes the function of a refrigerator in terms of thermodynamics?

Accepted Answer

It transfers heat from a cold reservoir to a hot reservoir using work.

Question 19

A heat engine using a diatomic gas follows the cycle shown in the figure. If the engine runs at $$500$$ rpm, what is the power output if the work per cycle is $$120\ \mathrm{J}$$?

Accepted Answer

$$P = 1000\ \mathrm{W}$$

Physics Exam 1 Study Guide: Fluid Mechanics & Thermodynamics

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