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The heat capacity, often denoted as \( C_p \), is a crucial property in thermodynamics. It refers to the amount of heat needed to raise the temperature of a given quantity of a substance by one degree Kelvin. Each substance has its unique value of heat capacity, based on its molecular composition and phase. In our exercise, the gas mixture has components CO2, H2O, and N2. We must use the specific heat capacities of these gases at the temperature range involved (1600 K to 700 K) to calculate the heat removed.

To find the average heat capacity of the gas mixture, we can use the provided molar percentages as weights. For instance, if the heat capacities at constant pressure of CO2, H2O, and N2 are \(C_{p,\text{CO2}}\), \(C_{p,\text{H2O}}\), and \(C_{p,\text{N2}}\) respectively, the weighted average heat capacity \( C_{p,avg} \) would be:
\[ C_{p,avg}= 20\% \times C_{p,\text{CO2}} + 30\% \times C_{p,\text{H2O}} + 50\% \times C_{p,\text{N2}} \]
Once we have this value, we can use it to determine the heat removed by the gas mixture.

Enthalpy change is another key concept and is represented by \( \Delta H \). It represents the total heat content change of a system during a process at constant pressure. For the specified gas mixture, as it cools from 1600 K to 700 K, the enthalpy decreases.

Using the formula for heat removed, \[ Q = \text{n} \times \text{C}_{p,\text{avg}} \times (\text{T}_1 - \text{T}_2) \] and the calculated average heat capacity, we can determine the total heat removed as the gases cool. Here, \(Q \) is the heat removed, \(n \) is the number of moles, \( \Delta T \) is the temperature change, and \( \text{C}_{p,\text{avg}} \) is the average specific heat capacity.

The enthalpy change for each mole of the gas mixture, when it is cooled, leads us to understanding the amount of energy available to convert the entering water into vapor.

A phase transition involves changing from one state of matter to another, like ice melting to water or water boiling to steam. In our exercise, liquid water at its saturation point is converting to vapor. This requires energy, known as the latent heat of vaporization. At 35 bar, we determine the enthalpy values for the liquid and vapor phases of water from standard tables.

The heat required for the phase change per kilogram of water is: \[ Q_{\text{water}} = h_g - h_f \]
Here, \( h_f \) is the enthalpy of saturated liquid water, and \( h_g \) is the enthalpy of saturated vapor. By subtracting these values, we find out the energy needed to completely vaporize the water.

This phase transition is a crucial part of the problem because we are finding out how much water gets vaporized by the heat removed from the gas mixture.

A steady-state process is one where conditions don't change over time. For example, in our exercise, the system is exchanging heat with the boiler without any change in the system's properties like temperature or pressure over time. In this steady-state scenario, the mass flow rates in and out of the system must balance.

Since we are ignoring stray heat transfer and kinetic and potential energy changes, the energy entering the system must equal the energy leaving it. This principle helps simplify our calculations. It means that the heat absorbed by the water (turning it into vapor) must come directly from the heat removed from the gas mixture.

Understanding steady-state assumptions helps make clear why we can directly relate the heat loss from the gas to the phase change in the water.

The composition of a gas mixture can vastly affect thermodynamic calculations. In our exercise, the mixture consists of 20% CO2, 30% H2O, and 50% N2 by molar analysis.

Each of these gases has distinct thermal properties (like specific heat capacity) which influence the total heat capacity of the mixture. The calculations in thermodynamics often involve weighted averages where each component's contribution is proportional to its molar percentage.

This is why we calculate a weighted average heat capacity for the gas mixture in Step 2. It allows us to consider the different impacts of each gas type on the total heat capacity. Accurate gas mixture composition data ensures the accuracy of any subsequent thermodynamic calculations.