Question

Consider a gas turbine combustor with air as the working fluid. The flow enters the device at 500 K and leaves at 1400 K with a mass flow rate of 0.1 kg/s. The changes in kinetic energy and potential energy of the flow are neglected. Assuming \( C_p = 0.717 \, \text{kJ/kg-K} \) and \( R = 0.287 \, \text{kJ/kg-K} \), the rate of heat addition is  kW (rounded off to the nearest integer). 
 

Hint:

For heat transfer problems in gas turbines: 1. Use the formula \( Q = \dot{m} \cdot C_p \cdot (T_{\text{out}} - T_{\text{in}}) \) for steady-flow processes.
2. Ensure all temperatures are in Kelvin and specific heat is in consistent units.
3. Neglect changes in kinetic and potential energy unless explicitly mentioned.

Answer 1

Step 1: Recall the formula for heat transfer in a flow.
The rate of heat addition (\( Q \)) is given by: \[ Q = \dot{m} \cdot C_p \cdot (T_{\text{out}} - T_{\text{in}}), \] where: - \( \dot{m} = 0.1 \, \text{kg/s} \) (mass flow rate), - \( C_p = 1.0 \, \text{kJ/kg-K} \) (specific heat at constant pressure), - \( T_{\text{out}} = 1400 \, \text{K} \) (exit temperature), - \( T_{\text{in}} = 500 \, \text{K} \) (inlet temperature). Step 2: Substitute the values.
\[ Q = 0.1 \cdot 1.0 \cdot (1400 - 500). \] Simplify the temperature difference: \[ T_{\text{out}} - T_{\text{in}} = 1400 - 500 = 900 \, \text{K}. \] \[ Q = 0.1 \cdot 1.0 \cdot 900. \] Step 3: Perform the calculations.
\[ Q = 0.1 \cdot 900 = 90 \, \text{kW}. \] Conclusion: The rate of heat addition is \( 90 \, \text{kW} \).