An ideal gas is expanded from (p1, V1, T1) to (p2, V2, T2) under different conditions. The correct statement(s) among the following is(are)

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:

1. 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)
2. 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.
3. 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.
4. 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.
5. Final Considerations:
   • The type of process (isothermal, adiabatic, isobaric, or isochoric) dictates the relationship between pressure, volume, and temperature during the expansion.
6. 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.