Question

Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. What is the effect of superheating the steam to a higher temperature on

Short answer

Question: Explain the effects of superheating the steam to a higher temperature on the net work output, heat added, thermal efficiency, and mean effective pressure of a simple ideal Rankine cycle. Answer: Superheating the steam to a higher temperature in a simple ideal Rankine cycle generally results in increased net work output, increased heat added to the cycle, higher thermal efficiency, and greater mean effective pressure. This is because higher temperatures at the turbine inlet lead to higher enthalpy differences during expansion, thus generating more work. Furthermore, higher thermal efficiency indicates better performance from the cycle in converting heat to work.

Step-by-step solution

Identify the components of the Rankine cycle

The simple ideal Rankine cycle consists of a boiler, turbine, condenser, and pump. The working fluid is water.

Analyze the cycle without superheating

First, analyze the simple ideal Rankine cycle without superheating. This will give us the base values that we can later compare to the case with superheating.

Calculate the properties of the states 1, 2, 3, and 4

Using steam tables and the given boiler and condenser pressures, calculate the properties such as enthalpy (h), entropy (s), and temperature (T) for each state in the cycle.

Calculate net work output, heat added, thermal efficiency, and mean effective pressure for the base case

Use the properties calculated in step 3 and the following equations: - Net work output: \(W_{net} = W_t - W_p\) (turbine work - pump work) - Heat added: \(Q_{in} = h_2 - h_1\) (enthalpy difference between boiler inlet and outlet) - Thermal efficiency: \(\eta = \frac{W_{net}}{Q_{in}}\) - Mean effective pressure (MEP): \(MEP = \frac{W_{net}}{v_1(V_2 - V_1)}\) (using specific volume)

Analyze the cycle with superheating

Now, analyze the simple ideal Rankine cycle with superheating. Consider a higher temperature for superheating the steam.

Calculate the properties of the states 1', 2', 3', and 4'

Using steam tables and the given boiler and condenser pressures along with the superheating temperature, calculate the properties such as enthalpy (h), entropy (s), and temperature (T) for each state in the cycle with superheating.

Calculate net work output, heat added, thermal efficiency, and mean effective pressure for the superheated case

Use the properties calculated in step 6 and the same equations as used in step 4: - Net work output: \(W_{net} = W_t - W_p\) (turbine work - pump work) - Heat added: \(Q_{in} = h_{2'} - h_{1'}\) (enthalpy difference between boiler inlet and outlet) - Thermal efficiency: \(\eta = \frac{W_{net}}{Q_{in}}\) - Mean effective pressure (MEP): \(MEP = \frac{W_{net}}{v_{1'}(V_{2'} - V_{1'})}\) (using specific volume)

Compare the effects of superheating on the cycle properties

Compare the values of net work output, heat added, thermal efficiency, and mean effective pressure calculated for both cases (with and without superheating) to analyze the effect of superheating on the Rankine cycle.

Present the results graphically

Prepare a temperature-entropy (T-s) diagram and a pressure-enthalpy (P-h) diagram to illustrate the Rankine cycle for both cases: without superheating and with superheating. With the comparison of both cases, you can now explain the effects of superheating the steam to a higher temperature on the net work output, heat added, thermal efficiency, and mean effective pressure of the cycle.