(a) What is the pressure PB at point B?
(b) What is the net work done by the gas in completing one cycle A B C A?
(c) What is the entropy change SC - SB?
Provide numerical answers in SI units.
A planetesimal orbiting the Sun absorbs solar energy at a rate equal to the
solar flux at the orbital radius multiplied by the cross-sectional area of the
planetesimal multiplied by (1 - the albedo). The temperature of the
planetesimal can be estimated by setting the rate of solar energy absorption
equal to the rate at which the planetesimal is radiating energy.
(a) If we assume the planetesimal radiates as a black body, and the solar
luminosity is 3.8*1026 Watts, calculate the temperatures of
planetesimals as a function of distance from the Sun and albedo.
(b) For water ice, with an albedo of 0.35 and sublimation temperature of 200 K,
find the minimum distance from the Sun that a water ice planetesimal can remain
solid.
For reference, the Earth orbital radius is 1.5*1011 m.
(a) Find an expression for the variation in atmospheric pressure P with
elevation h above sea level assuming that the temperature of the atmospheric air
T and the acceleration due to gravity g are both constant with elevation and
that the atmospheric air is an ideal gas with molar mass M.
(b) Now if the pressure at sea level is P0 = 1 atm, calculate the
atmospheric pressure at the top of Clingmans Dome, which at 2025 m is the
highest point in the Great Smoky Mountains National Park. Assume that the
temperature remains constant at T = 20oC,
and the molar mass of air is M = 28.8*10−3 kg/mol. Give your
result in atm.
(c) Melting and boiling points depend on pressure. A good approximation for
the rate of change of the melting or boiling temperature with pressure is given by the Clausius-Clapeyron relation dT/dP
= T ∆V/L, where L is the latent heat of the substance (per kg) and T is the
melting or boiling temperature at standard pressure, and ∆V is the change in
volume (per kg).
To first order estimate the change in the boiling point of water on top of
Clingmans Dome. (For small changes of the melting point temperature
expand ∆T = (dT/dP)∆P.)
The density of steam at 1 atm and 100 oC is 0.59 kg/m3,
and the latent heat of vaporization for water (per kg) is 2264.7 kJ.
In a Wilson cloud chamber at a temperature of 20 degrees C, particle tracks
are made visible by causing condensation on ions by an approximately reversible
adiabatic expansion of the volume in the ratio final volume/initial volume = 1.375.
The ratio of the specific heats of the gas at constant pressure and at
constant volume is CP/CV = 1.41. Estimate the gas
temperature after the expansion.
An object of mass m and density ρ = (3/4)ρwater is fixed to the
bottom of an aquarium with a string and is fully submerged in water. The
aquariums sits on a truck bed and the truck is at rest.
(a) What is the tension in the string?
(b) The truck now is accelerating with acceleration of magnitude g/10
along a straight line. What is the tension in the string and what is the
angle θ the string makes with the vertical?
(c) What is the angle α the water's surface makes with the horizontal?
One mole of a monatomic ideal gas is driven around the cycle A B C A shown on the PV diagram below. Step AB is isothermic, with a temperature TA = 500 K. Step BC is isobaric, and step CA is isochoric. The volume of the gas at point A is VA = 1 liter, and at point B is VB = 4 liter.
(a) What is the pressure PB at point B?
(b) What is the net work done by the gas in completing one cycle A B C
A?
(c) What is the entropy change SC - SB?
Provide numerical answers in SI units.