Internal energy is the sum of the randomly distributed kinetic energies and potential energies of the particles in a body.
The internal energy of an object can be:
increase healing it , or by doing work on it
reduced by cooling it or if work is done by it.
According to the first law of thermodynamics , when work is done on or by an object and/or energy is transferred to or from it by heating.
when changing state:
its temperature stays constant
the kinetic energy of its particles does not change
its internal energy changes because the potential energy of its particles changes as forces between them change and bonds between them are made or broken.
Specific latent heat of fusion of a substance is the amount of energy needed to change 1kg of it from solid to liquid without a change in temperature.
Specific latent heat of vaporization of a substance is the amount of energy needed to change 1kg of a liquid to gas without a change in temperature.
The specific heat capacity of a substance c is the amount of energy needed to raise the temperature of 1kg of a substance by 1 kelvin or degree.
if a substance is heated using an electrical heater , the energy transferred to it can be calculated using:
E = IVt
E = electrical energy supplied in joules
I = current in A
V = p.d in V
t = heating time in s
Continuous flow heating is the process of heating a fluid by having it flow continuously over a heater.
energy transfer per second = power of heating = mass flow per second x specific heat capacity x change in temp.
one mole of any substance contains 6.02 x 10^23 particles of that substance.
the molar mass of a substance s the mass of one mol of that substance in kgmol^-1.
The molar mass of an element in g equal to its relative atomic or relative molecular mass , depending on whether their particles are atoms or molecules.
The molar mass of a compound in g can be calculated by adding in the relative atomic masses of its constituent atoms shown in its chemical formula.
Absolute zero is defined as 0 K on the kelvin scale.
To convert between kelvin and Celsius you add 273.15 to celsius.
Boyles law states that for a fixed mass of gas at constant temperature the pressure p and the volume V are inversely proportional :
p proportional to 1/v or pv
The pressure law states that for a fixed mass of gas at constant volume the pressure p and absolute temperature T are directly proportional:
p is proportional to temperature.
plotting data for p against t gives a straight line through the origin.
Charles law states that for a fixed mass of gas at constant pressure , the volume V and absolute temperature T are directly proportional.
The gas laws describe the behavior of gases using following quantities and units:
volume V in m^3
pressure p in Nm^-2 or pascals Pa
temperature T in K
number of atoms or molecules N
amount of gas n in mol
An ideal gas is a theoretical gas that obeys the experimental gas laws at all pressures and temperatures. The internal energy of a gas is only dependent on the kinetic energy of its particles ; they do not have any potential energy.
The energy transferred to increase or decrease the volume of a gas at a constant pressure is given by:
W = p x change in volume
Brownian motion is the random motion of small particles suspended in a fluid.
Brownian motion provided evidence for the existence of atoms. Albert Einstein showed mathematically that the jiggling motion of particles suspended in a fluid could be caused by random collisions with much smaller particles that are in constant random motion.
pressure is caused by the change in momentum of the molecules colliding with the container walls or surfaces.
temperature is proportional to the average kinetic energy of the molecules.
Boyles law:
the pressure of a gas at constant temp is increased by reducing its volume because the gas molecules travel a smaller distance between collisions with the container walls, so there are more collisions per second and a greater pressure.
The pressure law:
the pressure of a gas at constant volume is increased by raising its temperature because this raises the average kinetic energy of the molecules.
Charles law:
the volume of a gas at constant pressure is increased by raising its temperature because this raises the average kinetic energy of the molecules.
According to kinetic theory , an ideal gas considering of N identical molecules , each of mass m, in a container of volume V , the pressure of gas is given by the kinetic theory question:
pV = 1/3 Nm (crms)^2
To derive the kinetic theory equation , the following assumptions about an ideal gas are made:
all molecules are identical and the volume of one is negatable compared with the volume of gas.
molecules are in continual , random motion
newtons law can be applied to the molecules and there are enough molecules to apply statistical laws.
collisions between particles and walls are perfectly elastic.
With a cubic container:
if a molecule collides with the right-hand wall:
x-component of its velocity ,c , reverses and becomes -c but cy and c z remain the same
x-component of its momentum reverses and becomes -mc
change in the momentum of the particle is -mc -mc = -2mc
With a cubic container:
time t between successive impacts with this wall is the total distance to the opposite wall and back divided by the x-component of the velocity
t = 2l / c
number of collisions per second = 1/t = c/2l
With a cubic container:
force on the molecule is equal to its rate of change on momentum , which is equal to the momentum charge per collisions multiplied by the number of collisions per second.
according to newtons third law , the force on the molecule is equal to opposite to the force on the wall so force on wall
F = mc^2 / l
For a cubic container:
pressure on wall = mc^2 / volume
The ideal gas equation and the kinetic theory equation are equivalent to each other and show that:
average molecular kinetic energy of particles in a gas are directly proportional to its temperature in K