University of California, Berkeley

Physics 7B, Lecture 001, Spring 2009 (Xiaosheng Huang)

Midterm 1

Monday, 2/23/2009

6:00-8:00 PM

Name:______________________

SID: ________________________

D/L Section:_______________

GSI: ________________________

Physical Constants:

Avogadro's number, NA: 6.02×1023

Gas Constant, R: 8.315J/mol·K

Boltmann's Constant, kB: 1.38×10-23 J/K

Stefan-Boltzmann Constant, σ: 5.67×10-8 W/m2·K4

Specific heat for water: c=4.19×103 J/kg·oC

Heat of vaporization for water: LV=22.6×105 J/kg

Heat of fusion for water: LF= 3.33×105 J/kg

Standard Temperature and Pressure (STP): T=273K, P=1atm=1.01×105 Pa

Atomic mass unit (1u): 1.6605×10-27 kg

Note: You are allowed one formula sheet (3½ by 5, double sided) and a calculator

(without wireless capabilities). Do NOT just write down an answer in the answer box;

show your steps. Formulaic answers may only involve the quantities given in a problem

and constants. Good Luck!

#1

#2

#3

#4

Total

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1. (25 pts.) A spherical solid aluminum sphere with mass M, density

ρ

, specific heat c,

and emissivity e, floats in the vacuum of intergalactic space. The sphere is initially (t=0)

at temperature T1.

a) How long does it take for the aluminum sphere to cool to the cosmic microwave

background (CMB) temperature, T0, assuming T1>T0? (For this part, ignore the radiation

energy that the aluminum sphere will absorb from the (CMB)).

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Formulaic Answer:

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If!T1!=!300K!and!T0!=!2.7K!at!t=0!and!the!mass!of!the!aluminum!sphere!is!M=!100!kg,!

find!the!numerical!value!for!the!cooling!time.!!For!aluminum,!e!=!0.02,!!

ρ

!= 2.7×103!kg/m3,!and!c=!0.90!×103!J/kg•K.!

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Numerical Answer:

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For parts b) and c), take into consideration that the aluminum sphere will absorb radiation

energy from the CMB.

b) If the temperature of the aluminum sphere at time t is T, what is the net heat loss

(|Qnet loss|) of the aluminum sphere at this point?

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Formulaic Answer:

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!|Qnet loss| =!

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c) Find a differential equation whose solution is T(t), the temperature of the aluminum

sphere as a function of time, t.

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Formulaic Answer:

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2. (25 pts.) The mint flavor comes from menthol, which has a molecular mass of

M=156.27, in atomic units. A bottle of mint oil at thermal equilibrium with the air in a

room at STP is opened at one end of the room at t=0. Assume the menthol molecule is

spherical in shape with a radius of R=0.5nm. Also assume the air in the room consists

only of N2 (ignore the O2 part) and treat the N2 as a spherical molecule with radius

r=0.3nm. Ignore all intermolecular interactions except elastic collisions.

a) Find the number density (number of molecules per unit volume, N/V) of the N2 in the

room.

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Numerical Answer:

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b) Find the rms average speed, vrms, for menthol molecule.

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Formulaic Answer:

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