Respuesta :
The conservation of energy allows finding the relationship between pressure and temperature is:
- Pressure is directly proportional to the temperature of the alcohol in the gaseous state.
Pressure is defined by the relationship between force and area of application.
P =[tex]\frac{F}{A}[/tex]
Where P is the pressure, F is the force and A is the area.
In the case of alcohol in the gaseous state, the mechanical energy of the molecules is only kinetic energy, it is related to temperature by the Boltzmann equation.
Em = K = [tex]\frac{3}{2}[/tex] kT
½ m v² = 3/2 k T
v² = [tex]\frac{3 k T}{m}[/tex]
Where m is the mass, v the velocity of the particles, k the Boltzmann constant and T the absolute temperature.
From this equation we see that as the temperature increases, the speed of the alcohol molecules also increases.
Using the relationship between the impulse and the change of momentum we can find the mean force.
I = F t = Δp
Where I impulse, F is the force, t is the time, Δp is the change of momentum.
if we assume elastic collisions the amount of initial and final moment are equal.
[tex]F = \frac{2p}{t} \\F = \frac{2m}{t} v[/tex]
If we assume that the molecules go at a constant speed.
v = d / t
t = d / v
Let's substitute.
[tex]F = \frac{2m}{d} v^2[/tex]
We substitute in the pressure equation.
P = 2m / Ad v²
[tex]P = \frac{6k}{ A d} \ T[/tex]
In conclusion using the conservation of energy we can find the relationship between pressure and temperature is:
- Pressure is directly proportional to the temperature of the alcohol in the gaseous state.
Learn more here: brainly.com/question/20638378
