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Internal Energy Equation:
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The internal energy equation for an ideal monatomic gas is derived from kinetic theory and relates the internal energy of the gas to its temperature and number of moles. It represents the total energy contained within the system.
The calculator uses the internal energy equation:
Where:
Explanation: This equation applies specifically to ideal monatomic gases and represents the total kinetic energy of all the gas particles in the system.
Details: Calculating internal energy is fundamental in thermodynamics for understanding energy transfer, heat capacity, and the behavior of gases under different conditions.
Tips: Enter the number of moles, gas constant (default is 8.314 J/mol·K), and temperature in Kelvin. All values must be positive numbers.
Q1: Why is the factor 3/2 used in the equation?
A: The factor 3/2 comes from the equipartition theorem, which assigns (1/2)kT of energy per degree of freedom for each molecule. Monatomic gases have 3 translational degrees of freedom.
Q2: Does this equation work for all types of gases?
A: This specific equation applies only to ideal monatomic gases. For diatomic or polyatomic gases, the equation would have different coefficients due to additional rotational and vibrational degrees of freedom.
Q3: What are typical values for internal energy?
A: Internal energy values depend on the amount of gas and temperature. For example, 1 mole of gas at room temperature (298K) has approximately 3710 J of internal energy.
Q4: How does internal energy relate to temperature?
A: For ideal gases, internal energy is directly proportional to temperature. As temperature increases, the internal energy increases linearly.
Q5: Can this equation be used for real gases?
A: This equation is an approximation for ideal gases. Real gases may require more complex equations of state that account for intermolecular forces and molecular volume.