A room is initially at the outdoor temperature of 25°C. Now a large fan that consumes 200W of electricity when running is turned on. The heat transfer rate between the room and the outdoor air is given as Q = UA (Ti - To) where U = 6 W/m2 °C is the overall heat transfer coefficient, A = 30 m2 is the exposed surface area of the room, and Ti and To are the indoor and outdoor air temperatures, respectively. Determine the indoor air temperature when steady operating conditions are established

Answers

Answer 1

The indoor air temperature when steady operating conditions are established is 27.3 °C.

We can use the energy balance equation to solve for the indoor air temperature when steady operating conditions are established. The energy balance equation is:

Q = Qin - Qout + Qgen

where Q is the rate of heat transfer between the room and the outdoor air, Qin and Qout are the rates of heat transfer between the room and the inside and outside walls, respectively, and Qgen is the rate of heat generation due to the fan.

We can assume that the rate of heat transfer between the room and the inside wall is negligible since the room is initially at the outdoor temperature. Therefore, we have:

Q = -UA(Ti - To) + Qgen

Substituting the given values, we have:

Q = -6 × 30 × (Ti - 25) + 200

Simplifying, we get:

Ti - 25 = -1/36 (200 - 180Ti)

Solving for Ti, we get:

Ti = 27.3 °C

Therefore, the indoor air temperature when steady operating conditions are established is 27.3 °C.

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Related Questions

the construction industry has a large impact on societyand the gereration of wealth. dicuss the impact under the following heading

direct and indirect employment

the creation of weath

the impact of building on society

Answers

The construction industry has a significant impact on society and the generation of wealth in several ways:

1. Direct and indirect employment: The construction industry is a major employer, providing jobs to a large number of people. In addition to the direct employment of construction workers, the industry also creates indirect employment opportunities in related industries such as architecture, engineering, and building materials manufacturing. The industry also provides employment opportunities for people in other fields such as finance, marketing, and project management.

2. The creation of wealth: The construction industry contributes significantly to the creation of wealth in society. The industry generates revenue for construction companies and provides employment opportunities for workers, which leads to increased consumer spending and economic growth. Construction projects also create value by increasing the supply of housing, commercial real estate, and infrastructure, which can increase property values and stimulate economic activity in the surrounding areas.

3. The impact of building on society: The construction industry has a significant impact on society through the buildings and infrastructure it creates. Buildings and infrastructure provide essential services such as housing, transportation, and utilities, which are critical to the functioning of society. The construction industry also plays a role in shaping the physical environment and the character of communities. Buildings and infrastructure can have a positive impact on the quality of life of people who use them, and can also contribute to the cultural identity and heritage of a community.

Overall, the construction industry is a vital part of society and the economy, providing employment opportunities, generating wealth, and contributing to the physical and cultural landscape of communities.

A turbojet is flying with a velocity of 900 ft/s at an altitude of 20,000 ft, where the ambient conditions are 7 psia and 10°F. The pressure ratio across the compressor is 13, and the temperature at the turbine inlet is 2400 R. Assuming ideal operation for all components and constant specific heats for air at room temperature, determine (a) the pressure at the turbine exit, (b) the velocity of the exhaust gases, and (c) the propulsive efficiency

Answers

A turbojet operates under ambient conditions of 7 psi and 10°F at an altitude of 20,000 ft, flying with a velocity of 900 ft/s. The compressor has a pressure ratio of 13, and the turbine inlet temperature is 2400 R.

Assuming ideal operation and constant specific heats, we can determine the following:

(a) The pressure at the turbine exit is 7 psi.

To find the pressure at the turbine exit, first calculate the pressure at the compressor exit: P2 = P1 * pressure ratio = 7 psi x 13 = 91 psi. Since it's an ideal operation, the pressure ratio across the turbine is equal to the pressure ratio across the compressor. Therefore, the pressure at the turbine exit, P3 = P2 / 13 = 91 psi / 13 = 7 psi.

(b) Using the conservation of mass and energy, the temperature at the turbine exit can be calculated.

Then, apply the ideal gas equation and the continuity equation to find the velocity of the exhaust gases. However, without more specific information, the exact numerical value for the velocity cannot be determined.

(c) The propulsive efficiency depends on the velocity of the exhaust gases and the initial velocity of the aircraft.

The higher the difference between these two velocities, the higher the propulsive efficiency. In an ideal turbojet, the efficiency can be improved by minimizing the difference between the aircraft and exhaust velocities.

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Determine the takeoff of 2 x 12's needed for the floor framing and sum it all up into a total linear feet of 2 x 12's required. For example, ten - 2 x 12's at 12' would be 120 linear feet.

Answers

We would need approximately 466.48 linear feet of 2 x 12's for the floor framing

How to calculate the value

Total Length of Joists = (2 * 20) + (2 * 30) = 100 feet

Spacing in Inches = 16

Linear Feet = (100 / 12) * (16 / 16) = 8.33 feet per joist

Total Linear Feet = Linear Feet per Joist * Total Number of Joists

Therefore, the total linear feet of 2 x 12's needed for this floor would be:

Total Linear Feet = 8.33 * 56 = 466.48 feet

So we would need approximately 466.48 linear feet of 2 x 12's for the floor framing.

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