Because in a compressed gas particles are closer together, so the potential energy is larger, but since potential energy is negative, then the internal energy is lower
Explanation:
The internal energy of a gas is the sum of the potential energy (PE) and the kinetic energy (KE) of the molecules of the gas:
[tex]E=PE+KE[/tex]
The kinetic energy of the molecules is directly proportional to the temperature of the gas, T, and it only depends on the temperature: therefore, if we take two gases at the same temperature, then their molecules have the same kinetic energy, no matter if their volumes are different.
The potential energy of the molecules in a gas instead is the energy due to the intermolecular forces between the molecules. The closer the particles are in a gas, the stronger the intermolecular forces, the larger the value of the potential energy; however, potential energy has a negative value. This means that for a compressed gas (particles closer to each other), the potential energy is more negative, and therefore the total internal energy E of a compressed gas is less than that of a rarefied gas.
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