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phy131studiof15:lectures:finalp1sol [2015/12/02 09:30] mdawber [Question 4] |
phy131studiof15:lectures:finalp1sol [2015/12/02 09:36] mdawber [Question 6] |
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===== Question 5 ===== | ===== Question 5 ===== | ||

- | A. $v_{sound}=343\mathrm{m\,s^{-1}}$ | + | {{phy141f12finalq6fig.png}} |

+ | | ||

+ | The speed of sound in air is $v=331+0.6T\, \mathrm{ms^{-1}}$ where $T$ is the temperature in $^{\circ}$C. Two organ pipes of length 0.6m which are open at both ends are used to produce sounds of slightly different frequencies by heating one of the tubes above the room temperature of 20$^{\circ}$C. | ||

+ | | ||

+ | A. (5 points) What is the lowest frequency sound that can be produced in the room temperature pipe? | ||

+ | | ||

+ | $v_{sound}=343\mathrm{m\,s^{-1}}$ | ||

$f=\frac{v}{2l}=\frac{343}{2\times0.6}=285.8\mathrm{Hz}$ | $f=\frac{v}{2l}=\frac{343}{2\times0.6}=285.8\mathrm{Hz}$ | ||

- | B. See [[phy131studiof15:lectures:chapter18&#open_and_closed_pipes|here]]. | + | B. (5 points) Draw on the figure the form of the standing wave amplitude for both displacement and pressure that produces this sound. |

+ | | ||

+ | See [[phy131studiof15:lectures:chapter18&#open_and_closed_pipes|here]]. | ||

+ | | ||

+ | C. (5 points) To produce beats with a beat frequency of 1Hz with the sound produced in (a) using the first harmonic of the heated pipe what should the temperature of the heated pipe be? | ||

- | C. $\Delta f=1\mathrm{Hz}$ | + | $\Delta f=1\mathrm{Hz}$ |

$f_{T}=286.8\mathrm{Hz}$ | $f_{T}=286.8\mathrm{Hz}$ | ||

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$T=\frac{344.2-331}{0.6}=22\mathrm{^{o}C}$ | $T=\frac{344.2-331}{0.6}=22\mathrm{^{o}C}$ | ||

- | D. $f'=\frac{v_{sound}+v_{obs}}{v_{sound}}f$ | + | D. (5 points) At what speed should a person running toward the tubes be moving so that the sound from the room temperature tube has an apparent frequency equal to the actual frequency of sound produced by the heated tube. |

+ | | ||

+ | $f'=\frac{v_{sound}+v_{obs}}{v_{sound}}f$ | ||

$286.8=\frac{343+v_{obs}}{343}285.8$ | $286.8=\frac{343+v_{obs}}{343}285.8$ | ||

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$v_{obs}=1.2\mathrm{m\,s^{-1}}$ | $v_{obs}=1.2\mathrm{m\,s^{-1}}$ | ||

- | E. $f=2\times285.8=571.6\mathrm{Hz}$ | + | E. (5 points) What is the frequency of the second harmonic that the room temperature pipe produces? |

+ | | ||

+ | $f=2\times285.8=571.6\mathrm{Hz}$ | ||

===== Question 6 ===== | ===== Question 6 ===== | ||

- | A. $e=\frac{W}{Q_{H}}$ | + | {{phy141f12finalq8fig.png:400}} |

+ | | ||

+ | The diagram shows the P-V diagram for a 40% efficient ideal Carnot engine. Assume the gas used in this Carnot engine is an ideal diatomic gas. | ||

+ | | ||

+ | A. (5 points) For every Joule of work obtained from the engine, how much heat needs to be added to engine? | ||

+ | | ||

+ | $e=\frac{W}{Q_{H}}$ | ||

$Q_{H}=\frac{1}{0.4}=2.5\mathrm{J}$ | $Q_{H}=\frac{1}{0.4}=2.5\mathrm{J}$ | ||

- | B.$Q_{H}=W+Q_{L}$ | + | B. (b) (5 points) For every Joule of work obtained from the engine how much heat is lost to the environment? |

+ | | ||

+ | $Q_{H}=W+Q_{L}$ | ||

$Q_{L}=1.5\mathrm{J}$ | $Q_{L}=1.5\mathrm{J}$ | ||

- | C. $P_{B}V_{B}=nRT_{H}$ | + | C. (5 points) At points B and D the gas in the system has the same volume, but different temperatures. If the gas at point D is at twice atmospheric pressure, what is the pressure of the gas at point B? |

+ | | ||

+ | $P_{B}V_{B}=nRT_{H}$ | ||

$P_{D}V_{D}=nRT_{L}$ | $P_{D}V_{D}=nRT_{L}$ | ||

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$P_{B}=3.33P_{atm}$ | $P_{B}=3.33P_{atm}$ | ||

- | D. The expansion from B to C is adiabatic so $P_{B}V_{B}^{\gamma}=P_{C}V_{C}^{\gamma}$ | + | D. (5 points) If the volume of the gas at point B is 1L what is the volume of the gas at point C? |

+ | | ||

+ | The expansion from B to C is adiabatic so $P_{B}V_{B}^{\gamma}=P_{C}V_{C}^{\gamma}$ | ||

For a diatomic gas $\gamma=\frac{7}{5}$ | For a diatomic gas $\gamma=\frac{7}{5}$ | ||

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$V_{C}=3.6\mathrm{L}$ | $V_{C}=3.6\mathrm{L}$ | ||

- | E. $\Delta S=0\mathrm{\frac{J}{K}}$ | + | E. (5 points) How much does the net entropy of the engine and the environment change for every Joule of work done by this Carnot engine? |

+ | | ||

+ | | ||

+ | $\Delta S=0\mathrm{\frac{J}{K}}$ |