84 additional exercises
Calculate the height and surface area of a silo withr=10 m,R=15 m
andV=3500 m^3.
- Scripts
Radioactive decay of radioactive materials can be modelled by the equa-
tionA=A 0 ekt, whereAis the population at timet,A 0 is the amount
att= 0 , andkis the decay constant (k 60 ). Technetium-99 is a radioiso-
tope that is used in the imaging of the brain. Its half-life time is 6 hours.
Write a script to calculate the relative amount of Technetium-99 (A/A 0 )
in a patient body for 24 hours after receiving a dose. After determining
the value ofk, define a vectort=0:2:24and then calculate and plot the
corresponding values ofA/A 0.
- Scripts
The variation of vapour pressureP(in units of mm Hg) of benzene with
temperatures (in◦C) in the range 8 ◦C 6 T 680 ◦Ccan be modelled with
Constants for the the Antoine equation:
Antoine equation taken
from the Dortmund
Data Base.
log 10 P=A− B
C+T
For benzene, the values of the constants are as follows:A=6.87987,
B=1196.76,C=219.161. Write a script that calculates the vapour
pressure for various temperatures. The script should create a vector of
temperatures fromT = 8 ◦CtoT = 42 ◦Cin increments of 2 degrees,
and display a two-column table ofPandT where the first column is
temperatures in◦C, and the second column is the corresponding pressures
in mm Hg. The script should also plotPagainstTand use a logarithmic
axis forP.
- Scripts
The temperature dependance of the heat capacityCpof many gases can
be described in terms of a cubic equation:
Cp=a+bT+cT^2 +dT^3
The following table gives the coefficients of the cubic equation for four
gases.Cpis inJoules/(g mol)(◦C)andT is in◦C. Write a script to
calculate the heat capacity for each gas at temperatures ranging between
200 and 400◦Cat 20◦Cincrements. To present the results, create an 11× 5
matrix where the first column is the temperature, and second to fifth
columns are the heat capacities ofSO 2 ,SO 3 ,O 2 , andN 2 , respectively.
