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One kg of fluid enters the steady flow apparatus at a pressure of P1, velocity 16m/s and
specific volume 0.4 m3/kg. The Inlet is 30 m above the ground level. The fluid leaves the
apparatus at Pressure of P2, velocity of 275 m/s and specific volume 0.6 m3/kg. The outlet is
at the ground level. The total heat loss between the inlet and outlet is 10 KJ/kg of fluid. If 140
KJ/kg of work is done by the system, find the change in specific internal energy and indicate
whether this is a increase or decrease.
P1 = 6 Bar − {
√X5
849 } Pa ; P2 = 1 Bar + {+√99 − X
4
}Pa
x= 51
Using powers of 10, estimate the number of quantum states accessible to an outer electron on an atom, by estimating the size of an atom and knowing that typical binding energies are a few eV. (That is, if the kinetic energy is greater than a few eV then the electron is no longer on the atom.) The number of states = VrVp/h3.)
White dwarf stars are essentially plasmas of free electrons and free protons
(hydrogen atoms that have been stripped of their electrons). Their densities
are typically 5 × 10^9 kg/m3 (i.e., 10^6 times the average density of Earth).
Their further collapse is prevented by the fact that the electrons are highly
degenerate, that is, all the low-lying states are filled and no two identical
electrons can be forced into the same state.
(a) Estimate the temperature of this system. (Assume nonrelativistic electrons and that p2
f /2m = (3/2)kT .)
(b) Now suppose that the gravity is so strong that the electrons are forced
to combine with the protons, forming neutrons (with the release of a
neutrino). If the temperature remains the same, what would be the density
of this degenerate neutron star?
Thermal energies for nucleons in large nuclei are comparable with their
binding energies of about 6 MeV.
(a) To what temperature does this correspond?
(b) Within nuclear matter, identical nucleons are separated by about 2.6 ×
10^−15 m. What is roughly the minimum temperature needed for them
not to be degenerate (i.e., for the number of accessible states to be much
larger than the number of particles.)?
Consider a system of nonrelativistic electrons in a white dwarf star at a
temperature of 10^9 K. Very roughly, what would be their density if the system
is degenerate? How does this compare with typical electron densities in
ordinary matter of about 10^30 electrons/m3?
Consider a system of nonrelativistic electrons in a white dwarf star at a
temperature of 109 K. Very roughly, what would be their density if the system
is degenerate? How does this compare with typical electron densities in
ordinary matter of about 1030 electrons/m3?
Consider a system of two rolled dice, each having six possible states available
to it (six different numbers of dots showing upward). According to classical
statistics, how many different arrangements are available to this system
(a) if the dice are distinguishable,
(b) if the dice are identical.
(c) According to classical statistics, in what fraction of the total number of
different configurations do the two dice show the same number of dots?
(d) What is the true number of distinguishable configurations available to
two identical dice?
(e) For what fraction of the distinguishable configurations in (a) do the two
dice show the same number of dots?
Consider a system of three flipped coins. According to classical statistics,
how many different arrangements are available to this system:
(a) if the coins are distinguishable,
(b) if the coins are identical?
(c) For what fraction of the arrangements in (a) are all three heads or all
three tails?
(d) What is the true number of different heads/tails configurations available
to a system of three identical flipped coins?
(e) For what fraction of these arrangements are all three heads or all three
tails
Given the wavefunction of a standing wave: y(x,t) = A sin(πx)cos(2πt), where x and y are in meters and
t is in seconds. The position of the second anti-node from the end x = 0 is at:
Find the impulse response h[n] for a causal LTI discrete-time systems satisfying the given
difference equations and indicate whether the system is a FIR or an IIR system.
y[n] + y[n - 1] = x[n] - 2x [n - 1]
