Equation of state
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What defines an ideal gas in terms of pressure, volume, and temperature?
An ideal gas is defined by the relationship pV ∝ T, where p is pressure, V is volume, and T is the thermodynamic temperature (in Kelvin). This proportionality indicates that for a fixed amount of gas, the ratio of pV to T remains constant.
State the ideal gas equation using the amount of substance (number of moles).
The ideal gas equation, using the amount of substance (n), is pV = nRT, where p is pressure, V is volume, n is the number of moles, R is the ideal gas constant (8.31 J/mol·K), and T is the thermodynamic temperature.
State the ideal gas equation using the number of molecules.
The ideal gas equation, using the number of molecules (N), is pV = NkT, where p is pressure, V is volume, N is the number of molecules, k is the Boltzmann constant, and T is the thermodynamic temperature.
Define the Boltzmann constant (k) in terms of the ideal gas constant (R) and Avogadro's constant (Nᴀ).
The Boltzmann constant (k) is defined as the ideal gas constant (R) divided by Avogadro's constant (Nᴀ): k = R / Nᴀ. This constant relates the average kinetic energy of particles in a gas to the gas's temperature.
If you double the number of moles of an ideal gas in a closed container at constant volume, what happens to the pressure if the temperature remains constant?
If the number of moles (n) is doubled in a closed container at constant volume (V) and constant temperature (T), the pressure (p) will also double, according to the ideal gas law pV = nRT. Since V, R, and T are constant, p is directly proportional to n.
How does an increase in temperature affect the average kinetic energy of the molecules in an ideal gas?
An increase in temperature leads to an increase in the average kinetic energy of the molecules in an ideal gas. This is because temperature is directly proportional to the average kinetic energy of the gas molecules. This relationship is embodied in the kinetic theory of gases.
A container holds 2 moles of an ideal gas at 300K. If the volume is 0.02 m³, what is the pressure of the gas?
Using pV = nRT, we can calculate the pressure: p = nRT/V = (2 mol * 8.31 J/mol·K * 300 K) / 0.02 m³ = 249300 Pa (or 249.3 kPa).
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