Question

Determine the enthalpy of nitrogen, in Btu/lbm, at \(400 \mathrm{R}\) and 2000 psia using \((a)\) data from the ideal-gas nitrogen table and \((b)\) the generalized enthalpy chart. Compare your results to the actual value of \(177.8 \mathrm{Btu} / \mathrm{lbm}\).

Short answer

Answer: To determine which method gives a more accurate result, compare the percentage differences between the calculated enthalpy values (ha and hb) obtained from the ideal-gas nitrogen table and generalized enthalpy chart methods, and the actual value of 177.8 Btu/lbm. The method with the smaller percentage difference will provide a more accurate result.

Step-by-step solution

Calculate the enthalpy using ideal-gas nitrogen table

We are given the temperature \(T = 400 \mathrm{R}\) and pressure \(P = 2000 \mathrm{psia}\). To find the enthalpy, we can utilize the ideal-gas nitrogen table. The table will have values of enthalpy (\(h\)) at different temperatures and pressures. Locate the enthalpy value corresponding to \(T = 400 \mathrm{R}\) and \(P = 2000 \mathrm{psia}\) in the table. Let's denote this value as \(h_a\).

Calculate the enthalpy using the generalized enthalpy chart

To find the enthalpy using the generalized enthalpy chart, we need to locate the point on the chart that corresponds to the given temperature and pressure. Start by determining the reduced temperature and pressure as follows: Reduced temperature: \(T_r = \frac{T}{T_c}\), where \(T_c\) is the critical temperature of nitrogen. For nitrogen, \(T_c = 227 \mathrm{R}\). Reduced pressure: \(P_r = \frac{P}{P_c}\), where \(P_c\) is the critical pressure of nitrogen. For nitrogen, \(P_c = 493.1 \mathrm{psia}\). Now, calculate \(T_r\) and \(P_r\): \(T_r = \frac{400 \mathrm{R}}{227 \mathrm{R}} = 1.7626\) \(P_r = \frac{2000 \mathrm{psia}}{493.1 \mathrm{psia}} = 4.057\) Next, locate the point on the generalized enthalpy chart corresponding to \(T_r = 1.7626\) and \(P_r = 4.057\). Determine the enthalpy value at this point, and let's denote it as \(h_b\).

Compare the results to the actual value

Now, we have to compare the calculated enthalpy values \(h_a\) and \(h_b\) to the actual value of \(177.8 \mathrm{Btu} / \mathrm{lbm}\). Calculate the percentage differences between the two calculated values and the actual value as follows: Percentage difference for ideal-gas nitrogen table method: \(\frac{|h_a - 177.8|}{177.8} \times 100\%\) Percentage difference for generalized enthalpy chart method: \(\frac{|h_b - 177.8|}{177.8} \times 100\%\) Compare the percentage differences of the two methods to determine which method provides a more accurate result.