ANSWER :To determine the thermal efficiency of the Rankine cycle, we can use the formula for thermal efficiency, which is given by:
\[
\eta = \frac{W_{\text{net}}}{Q_{\text{in}}}
\]
Where:
- \( W_{\text{net}} \) is the net work output of the cycle.
- \( Q_{\text{in}} \) is the heat input to the cycle.
In a Rankine cycle:
- \( W_{\text{turbine}} = \text{enthalpy decrease in turbine} \)
- \( Q_{\text{out}} = \text{heat released in the condenser} \)
Given:
- The enthalpy decreases by 150 kJ/kg in the turbine.
- The heat released during condensation is 280 kJ/kg.
To find \( Q_{\text{in}} \), we note that the enthalpy decrease in the turbine is part of the work output and does not directly give us the heat input. However, the heat input in a Rankine cycle is typically the heat added in the boiler, which can be derived if we have the enthalpy values or the heat release values for the condensation.
### Steps to calculate thermal efficiency:
1. **Determine the work done by the turbine (\( W_{\text{turbine}} \)):**
\[
W_{\text{turbine}} = 150 \, \text{kJ/kg}
\]
2. **Determine the heat released in the condenser (\( Q_{\text{out}} \)):**
\[
Q_{\text{out}} = 280 \, \text{kJ/kg}
\]
3. **Use the principle of energy conservation in a cycle:**
\[
Q_{\text{in}} = W_{\text{net}} + Q_{\text{out}}
\]
Here, \( W_{\text{net}} \) is the work output of the cycle, which is the work done by the turbine minus the work consumed by the pump. For simplicity, let's assume the work consumed by the pump is negligible compared to the turbine work. So,
\[
W_{\text{net}} \approx W_{\text{turbine}}
\]
4. **Calculate the net work output:**
\[
W_{\text{net}} = 150 \, \text{kJ/kg}
\]
5. **Calculate the heat input (\( Q_{\text{in}} \)):**
\[
Q_{\text{in}} = W_{\text{net}} + Q_{\text{out}} = 150 \, \text{kJ/kg} + 280 \, \text{kJ/kg} = 430 \, \text{kJ/kg}
\]
6. **Determine the thermal efficiency (\( \eta \)):**
\[
\eta = \frac{W_{\text{net}}}{Q_{\text{in}}} = \frac{150 \, \text{kJ/kg}}{430 \, \text{kJ/kg}}
\]
\[
\eta = \frac{150}{430} \approx 0.349
\]
\[
\eta \approx 34.9\%
\]
Thus, the thermal efficiency of the Rankine cycle is approximately \( 34.9\% \).