To determine the heat transfer during the process:
Identify Initial State: The initial state of the air-water vapor mixture is at 1.5 bar, 120°C, with a specific humidity (φ) of 10% in a 35 m³ vessel.
Use Psychrometric Chart or Equations: Employ the psychrometric chart or thermodynamic equations to find the properties of the mixture at both initial and final conditions, considering pressure, temperature, and humidity.
Calculate Initial and Final Specific Volume: Determine the specific volume of the mixture at both initial and final states using the ideal gas law, accounting for the change in temperature and pressure.
Apply First Law of Thermodynamics: Use the first law of thermodynamics (Q = ΔU + W) to calculate heat transfer (Q) during the process. As the system is closed (no work exchange) and rigid, focus on internal energy change (ΔU).
Calculate Change in Internal Energy: Compute the change in internal energy using the specific volume and temperature changes. ΔU = m * (u2 - u1), where u represents specific internal energy and m is the mass of the mixture.
Determine Heat Transfer: Given ΔU, calculate the heat transfer (Q) using Q = ΔU. Ensure proper unit conversions for temperature (from Celsius to Kelvin) and volume (if necessary).
By following these steps and accurately calculating the change in internal energy of the air-water vapor mixture during the cooling process, you'll be able to determine the heat transfer (in kJ) in the closed vessel.