Question

Refrigerant-134a undergoes an isothermal process at \(40^{\circ} \mathrm{C}\) from 2 to \(0.1 \mathrm{MPa}\) in a closed system. Determine the work done by the refrigerant-134a by using the tabular (EES) data and the generalized charts, in \(\mathrm{kJ} / \mathrm{kg}\).

Short answer

Question: Determine the work done by refrigerant-134a during an isothermal process at 40°C, as it undergoes a change in pressure from 2 MPa to 0.1 MPa using tabular data (EES) and generalized charts.

Step-by-step solution

Identify the initial and final states of the refrigerant

The refrigerant R-134a undergoes an isothermal process which means that the temperature remains constant. The initial state is at 40°C and 2 MPa, while the final state is at 40°C and 0.1 MPa.

Determine specific volumes using tabular data (EES)

Look up the specific volumes (\(v\)) for the initial and final states in the R-134a tables in the EES for isothermal process at 40°C. Find corresponding values for the pressures of 2 MPa and 0.1 MPa. We can denote them as \(v_1\) and \(v_2\) respectively.

Determine specific enthalpies using tabular data (EES)

Look up the specific enthalpy values (\(h\)) for the initial and final states in the R-134a tables in the EES for isothermal process at 40°C. Find the corresponding values for the pressures of 2 MPa and 0.1 MPa. We can denote the initial and final specific enthalpy as \(h_1\) and \(h_2\) respectively.

Calculate the work done using tabular data

We can calculate the work done by the refrigerant (\(W_{12}\)) using the following formula, which is derived from the first law of thermodynamics: \(W_{12} = \int_{1}^{2} v \, dP\) If we assume polytropic expansion, integrating the above equation, we get: \(W_{12} = \frac{v_2-v_1}{n-1}\left(\frac{P_1}{v_1^n}-\frac{P_2}{v_2 ^n}\right)\) By using the specific volume values and specific enthalpy values for R-134a obtained from tabular data in EES, substitute the values of \(v_1\), \(v_2\), \(n\), and \(P_1\), \(P_2\) in the above equation to calculate the work done in kJ/kg.

Determine specific volumes using generalized charts

Look up the initial and final states in the generalized charts for isothermal process at 40°C. Find the corresponding values for the reduced pressures and reduced temperatures of 2 MPa and 0.1 MPa. Use the generalized volume chart to determine the specific volumes \(v_1\) and \(v_2\) for the initial and final states.

Determine specific enthalpies using generalized charts

Look up the initial and final states in the generalized enthalpy chart for isothermal process at 40°C. Find the corresponding values for the reduced pressures and reduced temperatures of 2 MPa and 0.1 MPa, and then the specific enthalpies \(h_1\) and \(h_2\) for the initial and final states.

Calculate the work done using generalized charts

Repeat the calculation of work done (\(W_{12}\)) in Step 4 using the specific volumes and specific enthalpy values obtained from the generalized charts. Compare the work done value calculated using tabular data (EES) to the value calculated using generalized charts.