Final answer:
To find the work done in an isothermal process, the initial pressure, volume, and final volume can be used with the provided formula. The total work done over the cycle involving isothermal expansion, isobaric compression, and isochoric return to initial conditions will be zero.
Step-by-step explanation:
To calculate the work done in an isothermal process where a gas expands from volume Vi to volume Vf, the formula W = nRTln(Vf/Vi) is used. Given that n (number of moles) is not directly provided in this specific question, we first need to find n by using the initial conditions of the gas and the ideal gas law PV = nRT. The initial pressure (Pi) is given as 2.10E2 kPa (which is 2.10E5 Pa when converted to Pascals), and the initial volume (Vi) is 0.0360 m³. Using R = 8.31 J/mol*K, we can rearrange the ideal gas law to solve for n: n = PiVi / (RT). However, we don't have the temperature (T), but since this is an isothermal process, we don't need the exact value because it will cancel out in the next step when calculating work (W). So we can express n in terms of T, which will then be used in the work formula. Inserting the values to find work done: W = (PiVi/R) * R * ln(Vf/Vi). Notice that R cancels out and we can simplify the equation to W = PiVi * ln(Vf/Vi). Substitute Pi = 2.10E5 Pa, Vi = 0.0360 m³, and Vf = 0.165 m³ into the equation to find the work done: W = 2.10E5 Pa * 0.0360 m³ * ln(0.165 m³ / 0.0360 m³). After calculating the above expression, we'd obtain the work done by the gas during the isothermal expansion. Total Work Done in the Cycle, When the gas is then compressed isobarically back to its initial volume, the work done on the gas is equal in magnitude but opposite in sign to the work done by the gas during the expansion. The return to initial conditions isochronally does no work, as the volume does not change. Therefore, the total work done over the entire cycle will be zero.