Question

An average (1.82 kg or \(4.0 \mathrm{lbm})\) chicken has a basal metabolic rate of \(5.47 \mathrm{~W}\) and an average metabolic rate of \(10.2 \mathrm{~W}(3.78 \mathrm{~W}\) sensible and \(6.42 \mathrm{~W}\) latent) during normal activity. If there are 100 chickens in a breeding room, determine the rate of total heat generation and the rate of moisture production in the room. Take the heat of vaporization of water to be \(2430 \mathrm{~kJ} / \mathrm{kg}\).

Short answer

Question: Determine the total heat generation (sensible and latent heat combined) and the rate of moisture production for a room of 100 chickens, given the metabolic rates for an average chicken during normal activity and the heat of vaporization of water. Solution: Step 1: Calculate the total sensible heat generation. Total Sensible Heat Generation = 3.78 W × 100 Total Sensible Heat Generation = 378 W Step 2: Calculate the total latent heat generation. Total Latent Heat Generation = 6.42 W × 100 Total Latent Heat Generation = 642 W Step 3: Calculate the total heat generation. Total Heat Generation = Total Sensible Heat Generation + Total Latent Heat Generation Total Heat Generation = 378 W + 642 W Total Heat Generation = 1020 W Step 4: Calculate the rate of moisture production. Rate of Moisture Production = (Total Latent Heat Generation) / (2430 × 10^3 W/kg) Rate of Moisture Production = (642 W) / (2430 × 10^3 W/kg) Rate of Moisture Production = 2.64 × 10^-4 kg/s The total heat generation is 1020 W, and the rate of moisture production is 2.64 × 10^-4 kg/s.

Step-by-step solution

Calculate the total sensible heat generation.

To find the total sensible heat generation, we first need to find the sensible heat generated by a single chicken during normal activity (3.78 W) and then multiply it by the number of chickens in the room (100). Total Sensible Heat Generation = Sensible Heat by One Chicken × Number of Chickens Total Sensible Heat Generation = 3.78 W × 100

Calculate the total latent heat generation.

Similar to step 1, to find the total latent heat generation, we will find the total latent heat of one chicken (6.42 W) during their normal activity and multiply it by the number of chickens in the room (100). Total Latent Heat Generation = Latent Heat by One Chicken × Number of Chickens Total Latent Heat Generation = 6.42 W × 100

Calculate the total heat generation.

Now, we need to find the total heat generated in the room by combining the total sensible heat and total latent heat generated by all the chickens. Total Heat Generation = Total Sensible Heat Generation + Total Latent Heat Generation

Calculate the rate of moisture production.

Now, we need to find the rate of moisture production. We are given the heat of vaporization of water (2430 kJ/kg), and we have the total latent heat generation (from step 2). To find the rate of moisture production, we have to convert the latent heat generation to kg/s and then multiply by the heat of vaporization of water for 1 kg of water. Rate of Moisture Production = (Total Latent Heat Generation) / (Heat of Vaporization of Water) Rate of Moisture Production = (Total Latent Heat Generation) / (2430 × 10^3 W/kg)

Key concepts

Basal Metabolic Rate

The basal metabolic rate (BMR) is the amount of energy expended while at rest in a neutrally temperate environment, and in a post-absorptive state (meaning that the digestive system is inactive, which requires about 12 hours of fasting in humans). For many living organisms, including chickens as in our exercise, BMR is the rate at which energy is used solely for maintaining the basic bodily functions such as cell creation, nutrient processing, and respiration.
In the example provided, a single chicken has a basal metabolic rate of 5.47 W, and when considering a room with 100 chickens, the basal BMR-related heat generation would be 547 W (since BMR for each chicken can be multiplied by the number of chickens). It's essential to understand that BMR is a continuous process vital for the survival of living beings and contributes to the total heat generation in a controlled environment like a breeding room.

Sensible Heat

Sensible heat refers to the amount of heat exchanged by a body or a thermodynamic system that results in a temperature change. This kind of heat can be felt and measured, which means the changes are sensible to a thermometer or human touch. For instance, when chickens are active, their bodies produce more heat than what's generated at the basal metabolic rate, hence the sensible heat.
To calculate the total sensible heat in a room with 100 chickens from our exercise, you would take the sensible heat generated by one chicken during normal activity (3.78 W) and multiply it by the number of chickens to find that the flock contributes 378 W of sensible heat. Understanding sensible heat is crucial for regulating the temperature in spaces like animal breeding rooms to keep the environment comfortable for the chickens.

Latent Heat

Latent heat is the energy absorbed or released by a substance during a phase change without a change in temperature. This type of heat is 'hidden', as it's not associated with a temperature difference, hence the term 'latent', meaning dormant or not immediately observable. In the context of our exercise, chickens also release latent heat as part of moisture evaporation when they respire and perspire.
To determine the total rate of latent heat generation by the 100 chickens, we multiply the latent heat of one chicken (6.42 W) by 100, totaling 642 W. The latent heat is a significant factor in the moisture content and humidity of the room, affecting both the animals' comfort and the room's conditions.

Heat of Vaporization

The heat of vaporization is the amount of energy required to convert one kilogram of a substance from a liquid phase into a vapor or gaseous phase at constant temperature and pressure. It is an important property of substances because it directly affects the energy required for phase changes. In the case of the chickens' exercise, the reference to the heat of vaporization of water (2430 kJ/kg) is essential to calculate the rate of moisture production, as it indicates the amount of energy needed for the water expelled by the chickens through latent heat to evaporate.
We apply this value to determine the moisture production rate by dividing the total latent heat generation by the heat of vaporization value, which yields the amount of water, in kilograms, that can be evaporated per second in the breeding room. This is significant for understanding the implications for ventilation and air conditioning systems within such environments.

Moisture Production

Moisture production in biological systems, such as animal breeding environments, refers to the generation of water vapor from living organisms' respiration and evaporation of sweat. This process not only relates to the humidity levels in the air but also plays a role in the overall thermal balance of the space. The rate of moisture production can be calculated using the total latent heat, as we've done for the chicken room scenario.
By dividing the total latent heat generated by the entire room of chickens (642 W or 642 J/s as 1 W = 1 J/s) by the heat of vaporization of water (2430 kJ/kg or 2430 x 10^3 J/kg), we get the mass of water vapor produced per second. The moisture production needs to be properly managed, as high levels of humidity can affect both animal welfare and the durability of building materials. The calculated production rate helps in designing appropriate ventilation and environmental control measures.