Final answer:
To calculate the work done by an expanding ideal gas, we use thermodynamic equations suited to the specific process type (isothermal, adiabatic, etc.). The number of moles, temperature, pressures, and heat capacities are factored into these calculations.
Step-by-step explanation:
To calculate the work (w) done on or by an ideal gas during expansion or compression, we use the principles of thermodynamics. Specifically, we'll look into the first law of thermodynamics, which relates the internal energy change of a system to the heat added to the system and the work done by the system.
For an isothermal process involving an ideal gas, the work done for expansion (or compression) can be determined using the equation
w = -nRTln(Vf/Vi), where n is the number of moles,
R is the ideal gas constant, and Vi and Vf are the initial and final volumes, respectively.
When looking at an adiabatic process, the work can be deduced from the change in internal energy, since no heat exchange occurs.
To calculate the work done in an adiabatic process,
use the equation w = ΔU (change in internal energy),
which for an ideal gas can be found as w = nCvΔT,
where Cv is the specific heat at constant volume.
In the given case, considering an expansion from a higher to lower pressure under a constant heat capacity, one would need to consider whether the process is isothermal, isobaric, adiabatic, or another type, to use the appropriate formulas for calculating work.