How do you calculate work for isothermal processes?

Question

Jeremiah Adams · Accepted Answer

The basic premise is constant temperature. For ideal gases, the change in internal energy #U# is a function of ONLY temperature. From the first law of thermodynamics, we must have: #overbrace(cancel(DeltaU))^("0 for "DeltaT = 0) = q + w# And the work #w# done by or on the system is equal to the heat flow #q# into or out from the system, respectively: #ul(w = -q)# This is the simplest case, and is shown here in further detail.

Owen Ambrose · Answer

undefined For an isothermal process, work is calculated using the formula: $W = -P \Delta V$, where $W$ is the work done, $P$ is the pressure, and $\Delta V$ is the change in volume.

Natalie Anton · Answer

undefined For an isothermal process, where the temperature remains constant, the formula to calculate work $ W $ is given by:

$$ W = nRT \ln\left(\frac{V_f}{V_i}\right) $$

Where:
- $ W $ is the work done by the gas during the process.
- $ n $ is the number of moles of the gas.
- $ R $ is the ideal gas constant ($ 8.314 \, \text{J/mol} \cdot \text{K} $).
- $ T $ is the temperature of the gas in Kelvin.
- $ V_i $ is the initial volume of the gas.
- $ V_f $ is the final volume of the gas.

This formula can be derived from the relationship between pressure, volume, and temperature in an ideal gas and the definition of work done in thermodynamics.