Density is the ratio of a substance's mass to its volume and can be expressed mathematically as
D=M/Vwhere D is density, M is mass, and V is volume.
In science, we will use Celsius or Kelvin temperature scales to describe temperature.
Celsius = Kelvin - 273.15
Kelvin + 273.15 = Celsius
Kelvin = Celsius + 273.15
Celsius + 273.15 = Kelvin
The volume of a gas is directly proportional to its temperature in kelvins if the pressure and number of molecules are constant.
The volume of a gas is inversely proportional to its pressure if the temperature and the number of molecules are constant.
Combined Gas Law
Pressure is inversely proportional to volume, or higher volume equals lower pressure. Pressure is directly proportional to temperature, or higher temperature equals higher pressure.
vf = vi + atwhere vf is final velocity, vi is initial velocity, a is acceleration, and t is elapsed time.
v(ave) = (vf+vi)/2where v(ave) is average velocity, vf is final velocity, and vi is initial velocity.
df = di + vit + 1/2at2
where df is the final, total displacement…
di is the initial displacement. (How far from whatever point of reference is the object when the thing starts accelerating?)…
vi is the initial velocity of the object at the beginning of the acceleration.
t is the elapsed time from the beginning of the acceleration until the end of the period being observed.
(vit accounts for the motion of the object based on its starting velocity. It keeps covering distance at the initial rate, and additionally, it accelerates and covers more distance.)
a is the acceleration and t is elapsed time.
Where F is force, a is acceleration, and m is mass, then:
F = ma
Work and Energy:
Work is found by
W = Fdwhere W is work, F is force applied (not net force!), and d is displacement/distance.
Kinetic energy (KE) is found with this equation:
KE = 1/2 mv2where KE is kinetic energy, m is mass and v is velocity.
The potential gravitational energy can be found with this equation:
PE = mghwhere PE is potential gravitational energy, m is mass, g is acceleration due to gravity, and h is height.
On earth, acceleration due to gravity is 9.8 (m/s)/s
The amount of elastic potential energy is determined by how hard it is to compress or stretch something and how far it is stretched or compressed.
The equation to find this is:
PE = 1/2kd2where PE is potential elastic energy, k is a constant specific to a particular stretchy thing (spring, rubber band, etc.) and d is the distance that it is stretched or compressed (sometimes x is used instead of d, as in the illustration)
Now to find heat, we can use the formula:
Q = mcΔTWhere Q is heat or thermal energy, m is mass, c is a number called specific heat that you either look up or calculate, and ΔT is the change in temperature.