Question

One mole of a perfect gas, for which the molar heat capacity at constant volume is 3 2 , initially at 20 ֯C and 1.0×106 Pa undergoes a two-stage transformation. For each of the stages described in the following list, calculate the final pressure, q, w, ΔU, and ΔH. Also, calculate the q, w, ΔU, and ΔH for the complete process. The gas constant is 8.3145 J/K mole. (a) The gas is expanded isothermally and reversibly until the volume doubles. (b) Beginning at the end of the first stage, the temperature is raised to 80 ֯C at constant volume.

Answer 1

To determine the thermodynamic properties during the two-stage process of a perfect gas, apply the first law of thermodynamics and the ideal gas law. Properties like final pressure, heat transfer, work done, change in internal energy, and enthalpy must be calculated based on the nature of the processes (isothermal or isochoric) and known constants.

Step-by-step explanation:

Thermodynamic Properties Calculation of a Two-Stage Transformation

The student is tasked with calculating various thermodynamic properties of a perfect gas during a two-stage process. Initially, the gas is at 20°C and 1.0×106 Pa. The properties to be calculated include final pressure (P), heat transfer (q), work done (w), change in internal energy (ΔU), and change in enthalpy (ΔH) for each stage, as well as for the entire process. The gas constant is given as 8.3145 J/K mole.

Stage 1: Isothermal Expansion

During an isothermal expansion, the temperature remains constant, and thus ΔU = 0. The work done (w) is equal to the negative product of gas constant (R), temperature (T), and the natural logarithm of the volume ratio (Vf/Vi). Heat transfer (q) will equal -w since ΔU is zero, and change in enthalpy (ΔH) will also be zero for an ideal gas during an isothermal process.

Stage 2: Isochoric Temperature Increase

When the temperature of a gas increases at constant volume (isochoric process), there is no work done (w = 0), and the change in internal energy (ΔU) can be calculated by multiplying the number of moles (n), molar heat capacity at constant volume (Cv), and the change in temperature (ΔT). Heat transfer (q) is equal to the change in internal energy (ΔU) because there is no work done in an isochoric process. The change in enthalpy (ΔH) is calculated by multiplying the number of moles (n), molar heat capacity at constant pressure (Cp), and the change in temperature (ΔT).

To calculate the final pressure, and the thermodynamic properties for the complete process, one would need to apply the first law of thermodynamics and the ideal gas law to each of the two stages.