USSC2001 Energy Lecture 3 Thermodynamics of Heat. Wayne M. Lawton Department of Mathematics National University of Singapore 2 Science Drive 2 Singapore 117543. Email [email protected] http://www.math.nus.edu.sg/~matwml/courses/Undergraduate/USC/2007/USC2001/ Tel (65) 6516-2749. 1.
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is force per unit area and measured in Pascal’s
Pascal's law : (päskälz') [key] [for Blaise Pascal], states that pressure applied to a confined fluid at any point is transmitted undiminished throughout the fluid in all directions and acts upon every part of the confining vessel at right angles to its interior surfaces and equally upon equal areas. Practical applications of the law are seen in hydraulic machines.
Standard atmospheric pressure is 101 325 Pa
The triple point of water
We define the temperature of a gas by
It is an empirical fact that T is the same for any two gases that are in thermal equilibrium with each other.
The ingenious mercury thermometer shown
below can measure T at constant volume
Questions How can constant volume be maintained at different temperatures? How can density be measured?
Reservoir that can be raised and lowered
Amadeo Avogado 1776-1856 suggested that all
gases contained the same number of molecules
for a fixed volume, pressure and temperature
# molecules =
# moles =
= # molecules in a mole
= the Boltzmann constant
= the gas constant
For an elastic collision between a molecule and a wall
so the formula on page 13 of Lecture 1
where the subscript n denotes the normal components.
1 collision changes wall momentum by
of an object with horizontal velocity component
on an area A wall in a length L cylinder
since it travels 2 L distance between
collisions alternating between the left and right walls.
Since 1 collision transfers momentum
the momentum transfer rate for 1 object is
and the momentum transfer rate for all particles is
Since momentum transfer rate = force,
gas is a fluid, and Pascal’s law implies that the force
of a fluid is normal to a surface, the pressure
(pressure is not a vector)
The unit of pressure is
Our discussion about pressure ignored collisions.
since the directions of the particles after collision are
very sensitive to the direction between their centers at
the time of contact, the directions are random, if x,y,z
are orthogonal coordinates with x horizontal then
where N is the number of particles, with equations
Combining with the ideal gas law
WORK W AND HEAT Q
W (and Q) depend on the thermodynamic process, described by a path, not only on initial&final states
Question Compute W for constant p and constant T
1st Law: There exists an internal energy function
such that during any
2nd Law: There exists an entropy function
such that during any thermodynamic process
1. Derive the relationship between the k and R on p 5.
2. Show that the pressure difference between heights
3. Use this pressure difference equation to show
that a container of gas having mass m weights mg.
4. Use the ideal gas law to compute the air pressure as a function of height above the ground. Assume that g is constant for this problem.
5. On p 13 show that if the gas expands by dV then E_int decreases by P dV. Do this by analysing the collisions of the molecules against the top wall of the container – which moves by a constant speed over some interval of time.