# Vacuum of Intergalactic Space - Physics for Scientist and Engineers - Past Paper, Exams for Engineering Physics. Anna University of Technology

## Engineering Physics

Description: These are the notes of Past Paper of Physics for Scientist and Engineers and its key important points are: Vacuum of Intergalactic Space, Cosmic Microwave, Radiation Energy, Numerical Value, Differential Equation, Molecular Mass, Atomic Units, Molecules Per Unit Volume
Showing pages  1  -  4  of  11
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:
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
!!
!
!!
!
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)).
!
!
!
!
!
!
!
!
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/kgK.!
!
!
!
!!
!
!!
!
!
!
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?
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!|Qnet loss| =!
!
!
c) Find a differential equation whose solution is T(t), the temperature of the aluminum
sphere as a function of time, t.
!
!
!!
!
!!
!
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.
!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!
!
!
b) Find the rms average speed, vrms, for menthol molecule.
!
!
!
!