Understanding the Factor of Evaporation in Boilers

The question asks about a specific ratio related to the heat absorbed by water in a boiler under different conditions. Let's break down the terms involved.

The ratio mentioned is:

$\frac{\text{Heat received by 1 kg of water under working conditions}}{\text{Heat received by 1 kg of water evaporated from and at 100 °C}}$

Let's define the terms in the ratio:

• Heat received by 1 kg of water under working conditions: This refers to the actual heat absorbed by 1 kg of water as it passes through the boiler, starting from the feedwater temperature and pressure, getting heated to saturation temperature, potentially becoming steam, and then potentially being superheated. This heat input leads to the formation of 1 kg of steam at the operating pressure and temperature. If the feedwater temperature is $T_{fw}$ and the enthalpy of steam produced is $h_s$, the heat received per kg is $h_s - h_{f(T_{fw})}$, where $h_{f(T_{fw})}$ is the enthalpy of saturated water at $T_{fw}$.
• Heat received by 1 kg of water evaporated from and at 100 °C: This refers to the heat required to change the phase of 1 kg of water from saturated liquid at 100 °C to saturated steam at 100 °C. This is equal to the latent heat of vaporization of water at 100 °C. This value is approximately $2257 \text{ kJ/kg}$ or $539 \text{ kcal/kg}$. This condition (from and at 100 °C) is considered a standard reference point.

Now let's look at the given options:

• Factor of evaporation: This is defined precisely as the ratio of the heat absorbed by 1 kg of water under actual boiler conditions (from the feedwater temperature to the final steam condition) to the latent heat of vaporization of water at 100 °C (the heat required to evaporate 1 kg of water from and at 100 °C). This definition perfectly matches the ratio described in the question.
• Boiler efficiency: This is the ratio of the total heat energy supplied to the steam produced (output) to the total heat energy supplied by the fuel burned (input). It's a measure of how effectively the fuel's energy is transferred to the water/steam. It is not a ratio comparing heat absorbed under working conditions to heat absorbed under standard evaporation conditions.
• Overall efficiency: This term is often used synonymously with boiler efficiency in this context, or it might refer to the efficiency of a larger system involving the boiler. It does not represent the specific ratio described.
• Evaporation efficiency: This is not a standard technical term used in this specific context. It might be a distractor or a loosely used term. The correct technical term for the ratio described is the factor of evaporation.

Based on the definitions, the ratio of heat received by 1 kg of water under working conditions to that received by 1 kg of water evaporated from and at 100 °C is known as the factor of evaporation.

Revision Table: Key Boiler Efficiency Terms

Additional Information on Boiler Performance

The factor of evaporation is an important parameter in evaluating boiler performance, especially when comparing boilers operating under different conditions. It essentially normalizes the heat absorption performance to a standard condition (evaporation from and at 100 °C). This standard condition corresponds to receiving the latent heat of vaporization at atmospheric pressure.

Related to the factor of evaporation is the concept of Equivalent Evaporation. Equivalent evaporation is defined as the mass of water that would be evaporated from and at 100 °C by the same amount of heat absorbed by the water under the actual boiler operating conditions. It is calculated by multiplying the actual mass of water evaporated by the factor of evaporation.

$\text{Equivalent Evaporation (kg/hr)} = \text{Mass of water evaporated (kg/hr)} \times \text{Factor of Evaporation}$

Using equivalent evaporation allows for a direct comparison of the steaming capacity of different boilers, regardless of their operating pressures, temperatures, or feedwater temperatures.

Boiler efficiency, on the other hand, is a measure of how well the energy from the fuel is utilized. While factor of evaporation relates to the quality of steam produced relative to a standard, boiler efficiency relates to the overall energy conversion process from fuel to steam.