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This sounds suspiciously like statistical thermodynamics, a graduate-level chemistry/physics class. You're probably best off consulting a good text, like McQuarrie's Statistical Thermodynamics.

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Q: How does a graph of average kinetic energy against kelvin temperature show that the quantities are proportional?
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The average speed of the molecules of a gas is proportional to the?

Temperature.


What does temperature have to do with energy?

no, temperature is one form of energy, heat.


How is the temperature of a substance affected by a change in the average kinetic energy of its molecules?

Directly proportional-- If average KE increases, temperature increases, and vice versa.


What is the kinetic energy of a gas molecule proportional to according to the kinetic theory?

The kinetic energy of a single gas molecule is not proportional to anything. The average kinetic energy of gas molecules is proportional to their absolute temperature.


According to the kinetic theory what is the kinetic energy of a gas molecule proportional to?

The kinetic energy of a single gas molecule is not proportional to anything. The average kinetic energy of gas molecules is proportional to their absolute temperature.


What determines the speed of the atoms and molecules of a substace?

Temperature is a measure of the average kinetic energy of an object. This is proportional to how quickly the particles move.


A physical property that tells you how hot or cold matter is. The average speed of the particle in a substance?

The average translational kinetic energy of a monotomic atom is directly proportional to the thermodynamic temperature of the atom. E=1.5 (kT) where k = the Boltzman Constant where T = The Thermodynamic Temperature in Kelvin since it is the average kinetic energy is applied... 0.5mv2 = 1.5kT T = (mv2)/3k where m is the mass of the atom and v is the speed of the particle. Thus, the thermodynamic temperature is proportional to the square of the velocity.


What is the percentage that hot water moves faster than cold water?

This will surely depend on how hot, or how cold. Convert the temperatures to absolute temperatures (Kelvin), then, assuming that the temperature is related to a great extent to the kinetic energy of the particles, the temperature would be proportional to the kinetic energy, or: the temperature is proportional to the square of the average particle speed. For example, under these assumptions, a 10% increase (factor 1.1) in the average particle speed would correspond to a 21% (factor 1.21) increase in the absolute temperature.


How is heating related to a substance's temperature?

As an object is heated, the rate of increase in temperature is proportional to the rate of heat added. The proportionality is called the heat capacity. Because the heat capacity is actually a function of temperature in real materials, the total amount of energy added will be equal to the integral of the heat capacity function over the interval from the initial temperature to the final temperature. If you just assume an average heat capacity over the temperature range, then the rise in temperature will be exactly proportional to the amount of heat added.


Temperature is proportional to the average kinetic energy of particles in an object thus an increase in temperature results in a?

Thermodynamic temperature (absolute temperature) is proportional to the averagekinetic energy of particles in "gases". An increase in temperature will increase theaverage kinetic energy of the particles of the gas and at the same time the particle'skinetic energy distribution gets broader.If pressure of the gas is kept constant, the gas expands (increases its volume).If the volume of the gas is kept constant, the gas pressure increases.


The temperature scale defined so that temperature of a substance is directly proportional to the average kinetic energy of particles and so that zero on the scale corresponds to zero kinetic energy?

This is the thermodinamic scale (Kelvin scale).


How is heating related to a substance?

As an object is heated, the rate of increase in temperature is proportional to the rate of heat added. The proportionality is called the heat capacity. Because the heat capacity is actually a function of temperature in real materials, the total amount of energy added will be equal to the integral of the heat capacity function over the interval from the initial temperature to the final temperature. If you just assume an average heat capacity over the temperature range, then the rise in temperature will be exactly proportional to the amount of heat added.