Question

Steam is throttled from 7 MPa and \(500^{\circ} \mathrm{C}\) to a pressure of 1 MPa. Determine the decrease in exergy of the steam during this process. Assume the surroundings to be at \(25^{\circ} \mathrm{C} .\)

Short answer

Question: Calculate the decrease in exergy of steam during a throttling process. The process starts with the steam at 7 MPa and \(500^{\circ} C\) and ends with the steam pressure at 1 MPa. The given surrounding temperature is \(25^{\circ} C\). Assume the steam table values of enthalpy, entropy, and specific volume for both initial and final states. Provide the step by step solution with appropriate formulae. Answer: The decrease in exergy during the throttling process can be calculated in several steps. 1. Identify the specific properties of steam at the initial state (7 MPa and \(500^{\circ} C\)) and at the final state (1 MPa) from the provided steam tables. The properties include enthalpy, entropy, and specific volume. 2. Compute the initial exergy (\(e_1\)) using the formula: \(e_1 = h_1 - T_0 s_1 - P_0 v_1\), where \(T_0 = 298.15K\) is the surrounding temperature and \(P_0 = 0.1 MPa\) is the atmospheric pressure. 3. Compute the final exergy (\(e_2\)) using the same formula: \(e_2 = h_2 - T_0 s_2 - P_0 v_2\). Note that \(h_2 = h_1\) due to the isenthalpic nature of the throttling process. 4. Calculate the decrease in exergy (\(\Delta e\)) by subtracting \(e_2\) from \(e_1\). Therefore, \(\Delta e = e_1 - e_2\).

Step-by-step solution

Identify the initial and final state of the steam in the steam tables

Using the initial and final conditions given, the steam is first at 7 MPa and \(500^{\circ} \mathrm{C}\). We can use these values in the steam tables to look for the corresponding initial enthalpy (\(h_1\)), initial entropy (\(s_1\)), and specific volume (\(v_1\)) at this condition. Similarly, we need to find the enthalpy (\(h_2\)), entropy (\(s_2\)), and specific volume (\(v_2\)) of the steam at the final pressure of 1 MPa. Since the throttling process is an isenthalpic process, we can assume that the enthalpy does not change (\(h_1 = h_2\)).

Calculate initial exergy of steam using the given parameters

Using the values of \(h_1\), \(s_1\), and \(v_1\) from the steam tables, we will compute the initial exergy using the following equation: \(e_1 = h_1 - T_0 s_1 - P_0 v_1\) where: \(e_1\) is the initial exergy, \(T_0\) is the surrounding temperature (which is given as \(25^{\circ} \mathrm{C}\), or in Kelvin, \(T_0 = 273.15 + 25 = 298.15\,\mathrm{K}\)), \(P_0\) is the atmospheric pressure (which can be assumed as 100 kPa or 0.1 MPa).

Calculate final exergy of steam using the given parameters

Similarly, using the values of \(h_2\), \(s_2\), and \(v_2\), we will compute the final exergy using the same equation as for the initial exergy: \(e_2 = h_2 - T_0 s_2 - P_0 v_2\) where: \(e_2\) is the final exergy. Note that \(h_2 = h_1\) since it is a throttling (isenthalpic) process.

Calculate decrease in exergy

The decrease in exergy during this throttling process is the difference between the initial and final exergy: Decrese in exergy (\(\Delta e\) ) = \(e_1 - e_2\) By obtaining the values of \(e_1\) and \(e_2\) from the previous steps, and finding the difference between these two values, the decrease in exergy of steam during the throttling process will be calculated.