When an ideal gas expands under different conditions, the relationship between the pressure, volume, and temperature changes according to the ideal gas law. Here's the explanation for the possible statements:
- Use the Ideal Gas Law:
- The ideal gas law is given by:
pV = nRT, where:
- p = pressure of the gas
- V = volume of the gas
- n = number of moles of the gas
- R = universal gas constant
- T = temperature of the gas (in Kelvin)
- Is the gas undergoing isothermal expansion?
- If the gas expands isothermally, the temperature remains constant (T1 = T2). In this case, according to the ideal gas law,
p1V1 = p2V2 because T1 = T2.
- This means that the pressure decreases when the volume increases, and vice versa, for an isothermal expansion.
- Is the gas undergoing adiabatic expansion?
- If the gas expands adiabatically (no heat exchange), the relationship between pressure, volume, and temperature is governed by the adiabatic equation:
pV^γ = constant, where γ is the heat capacity ratio (Cp/Cv).
- In this case, both pressure and temperature decrease as the volume increases, and this is a faster change than in an isothermal process.
- Is the gas undergoing isobaric or isochoric expansion?
- If the gas is expanded at constant pressure (isobaric process), the temperature and volume change proportionally according to
pV = nRT, so V1/T1 = V2/T2.
- If the gas is expanded at constant volume (isochoric process), the pressure and temperature change proportionally, following
p1/T1 = p2/T2.
- Final Considerations:
- The type of process (isothermal, adiabatic, isobaric, or isochoric) dictates the relationship between pressure, volume, and temperature during the expansion.
- Final answer:
The correct statement(s) would depend on the specific conditions of the gas expansion (whether it is isothermal, adiabatic, isobaric, or isochoric). Each process has its own governing equations.
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