Chapter 7 Concept Test Answers
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Chapter 7 Concept Test Answers
CT-1 A system S is in thermal contact with a heat bath at temperature T. The system can exchange energy only with the bath. Consider two quantum states of the system: state 1 with low energy E1 state 2 with high energy E2
P(state 1) The ratio of the probabilities is ... P(state 2) A) always greater than 1 B) always less than 1 C) greater, less than, or equal to one, depending on the temperature.
Answer: always greater than 1. The Boltzmann relation says that a particular state of lower energy is always more probable than a particular state of higher energy. This does NOT, does NOT mean that lower energies are always more probable than higher energies. Do not confuse probability of a state with probability of an energy.
Bath T
system
CT-2 If the temperature T is increased, the probability P(i) that the system is in a particular quantum state i (say, i = 6) will A) decrease B) increase C) remain constant D) not enough info to answer question
Answer: not enough info to answer the question. Whether P(i) increases or decreases with increasing temperature depends on the value of the energy Ei and the starting temperature. CT-3 An ideal gas is in a container divided into two halves. Initially, the two samples of gas are identical. Some more particles are added to the sample on the left, keeping the temperature constant. The chemical potential on the left.. A) increases B)decreases C) stays the same as the chemical potential on the right
Answer: increases Recall that particles always diffuse from higher chem.pot. to lower chem.pot.
CT-4 An atom (say an H-atom) is sitting in a gas of electrons with temperature T and chemical potential The atom can either be in its ground state or be ionized (occupied or empty). [We pretend that excited states can be ignored.] If the chemical potential is lowered (made more negative), while the temperature is maintained at a very low value (kT< Answer: increases. CT-5 Which has the larger fermi energy: A small piece of copper and a large piece of copper? A) larger piece has the larger fermi energy B) smaller piece has the smaller fermi energy C) fermi energy is the same for both pieces Answer: fermi energy is the same for both pieces CT-6 If a quantum particle in a box is compressed, what happens to the energy of the particle? A) energy remains constant B) energy increases C) energy decreases Answer: B) energy increases CT-7 About how long has the sun been shining? A)50 millions years B) 500 million years C) 5 billion yrs D) 50 billion yrs E)500 billion years Answer: About 5 billion yrs CT-8 If more mass is added to the surface of a white dwarf, the diameter of the star gets... A) larger B) smaller C) stays the same [White dwarf stars are frequently members of a binary star system and stellar matter from the other star falls into the white dwarf.] Hint: M R F M2 / R 2 M 2 p = : : gravity A R2 R 4 UN N骣 N2/ 3 骣 N 5 / 3 骣 M 5 / 3 M5/ 3 eF 珑 鼢 pdegeneracy : : :珑 鼢 : :3 : 5 V V V桫珑 V鼢 桫 V 桫 R R Answer: Smaller. Equilibrium is achieved when pgravity = pdengeneracy, which implies M2 M 5/ 3 R5 M 5/ 3 1 : or :, or R : R4 R 5 R4 M 2 M 1/ 3 CT-9What is the relation between frequency, wavelength and speed c of a sinusoidal traveling wave? c l A) f = B) f= l c C) f = l c D) None of these c Answer: f = l CT-10 A standing wave (not necessarily the one shown) has wavelength . What is the frequency f of the standing wave? c 2 c A) B) l C) l l c 2 D) depends on how many nodes are in the standing wave E) none of these c Answer: f = (same as for a traveling wave) l 1 CT-11 What does the Planck distribution function n = ehf / kT - 1 look like, as a function of temperature? n n A B kT/hf kT/hf n n C D kT/hf kT/hf Answer: A CT-12Two balls are suspended in the interior of an oven at temperature T. The balls are identical, except one is painted white and the other is painted black. Which ball emits more radiation? A) The black ball emits more. B) The white ball emits more. C) They both emit the same amount. T Answer: the black ball emits more. For each ball, the rate of absorption must equal the rate of emission. So a good absorber is a good emitter. A poor absorber is a poor emitter. CT-13An oven at temperature T has a small hole in it. A tunnel with perfectly reflective walls connects the hole to a surface that is perfectly black (absorbs all light hitting it). In equilibrium, all interior surfaces are at temperature T. Black surface T Reflecting walls How does the power emitted by the black surface compare with the power emitted by the hole into the reflective tunnel. A) Power emitted by black surface = power from hole B) Power emitted by black surface > power from hole C) Power emitted by black surface < power from hole Answer: Power emitted by black surface = power from hole CT-14 Consider a thin shell of constant radius in “m-space”. Each point in m-space corresponds to a normal mode of the radiation within an oven. True(A) or False(B): m All the modes in this shell (m m+dm) have the same z average energy E. Answer: True True(A) or False(B): the average energy E of the modes m in the shell depends on temperature. y Answer: True m x True(A) or False(B): All the modes in this shell have the same frequency f. Answer: True True(A) or False(B): for all the modes in this shell, Emode = hf, where Emode is the average energy of the mode and f is the frequency of the mode. Answer: FALSE! Emode = nhf, where n is the number of photons in the mode. CT-15The energy spectrum u(e ) of blackbody radiation is defined the by the relation U tot . What are the units of ? utot == u( e )d e u(e ) V A) power = energy/time B) (volume)1 C) energy/volume D) (energyvolume)1 E) None of these Answer: (volume)1 CT-16The wavelength spectrum u(l ) of blackbody radiation is defined the by the U relation tot . What are the units of ? utot == u( l )d l u(l ) V A) power = energy/time B) (volume)1 C) energy/volume D) (energyvolume)1 E) None of these Answer: None of these. The units of u(l ) are energy/(volumelength).