- #1
Hardik Batra
- 130
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Why the kinetic energy is same as internal energy of ideal gas?
Matterwave said:In an ideal gas (that we regularly study), there is assumed to be no interactions between the gas molecules. No interactions means no potential energy, so the only form of energy left is kinetic.
Hardik Batra said:No interaction means no potential energy how?
jtbell said:Potential energy is defined in terms of an interaction force, specifically a conservative force.
$$V(P) = - \int_{P_0}^P {\vec F \cdot d \vec r}$$
Hardik Batra said:Why the kinetic energy is same as internal energy of ideal gas?
Kinetic energy is the energy that an object possesses due to its motion. In an ideal gas, kinetic energy refers to the energy that gas molecules have as they move and collide with each other. Internal energy, on the other hand, is the total energy of a gas system, including both kinetic and potential energy of the molecules.
In an ideal gas, the molecules are considered to be point masses that do not interact with each other except through collisions. This means that all the energy in the system is in the form of kinetic energy, as there is no potential energy between the molecules. Therefore, the total kinetic energy of the molecules is equal to the total internal energy of the gas.
The temperature of an ideal gas is directly proportional to the average kinetic energy of its molecules. This is because temperature is a measure of the average kinetic energy of the molecules. Therefore, as the temperature of an ideal gas increases, so does the kinetic energy and internal energy of its molecules.
In an ideal gas, the kinetic energy and internal energy are always the same. This is because an ideal gas follows the ideal gas law, which states that the internal energy of a gas is directly proportional to its temperature. As mentioned earlier, temperature is a measure of the average kinetic energy of the gas molecules, so the internal energy and kinetic energy are always equal in an ideal gas.
In an ideal gas, the kinetic energy and internal energy do not change with pressure and volume, as long as the temperature remains constant. This is because the ideal gas law (PV = nRT) states that pressure and volume are inversely proportional, and temperature is directly proportional to the internal energy. So, as pressure and volume change, the temperature also changes in such a way that the internal energy remains constant, and therefore the kinetic energy remains the same as well.