What's the thermal energy of one mole of ideal gas at 0^∘ C ? (a) 0 J ; (b) 1700 J (c) 2200 J

step 1 The average thermal energy formula is given by E -tas is equal to 3x2 N -A K -B -T. This is the

What's the thermal energy of one mole of ideal gas at 0^∘ C...

Key Concepts

Internal Energy of Ideal Gases

In thermodynamics, the internal energy of an ideal gas is the sum of the kinetic energies of its molecules, and it depends only on temperature rather than pressure or volume. For a monatomic ideal gas, the internal energy per mole is given by U = (3/2)RT, where R is the gas constant and T is the absolute temperature. This concept is fundamental in relating macroscopic observations to microscopic kinetic motion.

Equipartition Theorem

The equipartition theorem states that, at thermal equilibrium, energy is distributed equally among all accessible degrees of freedom. Each quadratic degree of freedom contributes (1/2)kT per molecule (or (1/2)RT per mole) to the internal energy. This theorem explains why the internal energy of an ideal gas is directly proportional to its temperature and is key to understanding energy distributions in gases.

Ideal Gas Law and Molar Quantities

The ideal gas law, expressed as PV = nRT, connects pressure, volume, temperature, and number of moles. This law is critical when analyzing the behavior of gases and allows the use of molar quantities, such as the idea that one mole of an ideal gas at a given temperature has a predictable internal energy. It provides the framework for applying thermodynamic formulas to real and idealized gas systems.

Temperature Conversion in Thermodynamics

Thermodynamic calculations require the use of the absolute temperature scale (Kelvin), as physical laws such as those governing energy depend on an absolute measure of thermal energy. Converting Celsius to Kelvin by adding 273.15 ensures that temperature values are properly scaled for use in equations like U = (3/2)RT, which yields accurate results in energy calculations.

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