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A thin metal plate of 4 cm diameter is suspended in atmospheric air whose temperature is 290 K. This plate attains a temperature of 295 K when one of its face receives radiant energy from a heat source at the rate of 2 W. If heat transfer coefficient on both surfaces of the plate is stated to be 87.5 W/m 2 K, workout the reflectivity of the plate
- a)0.35
- b)0.45
- c)0.55
- d)0.65
Correct answer is option 'B'. Can you explain this answer?
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A thin metal plate of 4 cm diameter is suspended in atmospheric air wh...
Heat loss by convection from both sides of the plates = 2 h A d t = 1.1 W. Energy lost by reflection = 2.0 – 1.1 = 0.9 W.
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A thin metal plate of 4 cm diameter is suspended in atmospheric air wh...
To solve this problem, we need to use the concept of energy balance. The energy balance equation for the plate can be written as:
Energy In = Energy Out
The energy in is the radiant energy received from the heat source, which is given as 2 W. The energy out can be calculated using the Stefan-Boltzmann law, which states that the rate of energy emitted by a black body is proportional to the fourth power of its temperature.
Now, let's break down the problem into steps:
Step 1: Calculate the energy emitted by the plate
We know that the energy emitted by a black body is given by the equation:
Energy = σ * A * (T^4)
Where σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4), A is the surface area of the plate, and T is the temperature of the plate in Kelvin.
Since the plate is thin and circular, we can assume both sides have the same surface area. So the total surface area of the plate is:
A = π * r^2 = π * (0.02 m)^2 = 0.00126 m^2
Using this value, we can calculate the energy emitted by the plate at 295 K:
Energy out = σ * A * (T^4) = 5.67 x 10^-8 * 0.00126 * (295^4) = 2.35 W
Step 2: Calculate the energy absorbed by the plate
Since the plate is in a surrounding environment at a temperature of 290 K, it will absorb energy from the surroundings due to the temperature difference. The energy absorbed is given by the equation:
Energy absorbed = h * A * (T - Ts)
Where h is the heat transfer coefficient, A is the surface area of the plate, T is the temperature of the plate, and Ts is the temperature of the surroundings.
Using the given values, we can calculate the energy absorbed by the plate:
Energy absorbed = 87.5 * 0.00126 * (295 - 290) = 0.55 W
Step 3: Calculate the reflectivity of the plate
The reflectivity of the plate can be calculated by subtracting the absorbed energy from the total energy received and dividing by the total energy received:
Reflectivity = (Energy in - Energy absorbed) / Energy in
Plugging in the values, we get:
Reflectivity = (2 - 0.55) / 2 = 0.725
Therefore, the reflectivity of the plate is approximately 0.73. None of the given options match this value, so there might be an error in the problem statement or in the provided answer options.
Energy In = Energy Out
The energy in is the radiant energy received from the heat source, which is given as 2 W. The energy out can be calculated using the Stefan-Boltzmann law, which states that the rate of energy emitted by a black body is proportional to the fourth power of its temperature.
Now, let's break down the problem into steps:
Step 1: Calculate the energy emitted by the plate
We know that the energy emitted by a black body is given by the equation:
Energy = σ * A * (T^4)
Where σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4), A is the surface area of the plate, and T is the temperature of the plate in Kelvin.
Since the plate is thin and circular, we can assume both sides have the same surface area. So the total surface area of the plate is:
A = π * r^2 = π * (0.02 m)^2 = 0.00126 m^2
Using this value, we can calculate the energy emitted by the plate at 295 K:
Energy out = σ * A * (T^4) = 5.67 x 10^-8 * 0.00126 * (295^4) = 2.35 W
Step 2: Calculate the energy absorbed by the plate
Since the plate is in a surrounding environment at a temperature of 290 K, it will absorb energy from the surroundings due to the temperature difference. The energy absorbed is given by the equation:
Energy absorbed = h * A * (T - Ts)
Where h is the heat transfer coefficient, A is the surface area of the plate, T is the temperature of the plate, and Ts is the temperature of the surroundings.
Using the given values, we can calculate the energy absorbed by the plate:
Energy absorbed = 87.5 * 0.00126 * (295 - 290) = 0.55 W
Step 3: Calculate the reflectivity of the plate
The reflectivity of the plate can be calculated by subtracting the absorbed energy from the total energy received and dividing by the total energy received:
Reflectivity = (Energy in - Energy absorbed) / Energy in
Plugging in the values, we get:
Reflectivity = (2 - 0.55) / 2 = 0.725
Therefore, the reflectivity of the plate is approximately 0.73. None of the given options match this value, so there might be an error in the problem statement or in the provided answer options.
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A thin metal plate of 4 cm diameter is suspended in atmospheric air whose temperature is 290 K. This plate attains a temperature of 295 K when one of its face receives radiant energy from a heat source at the rate of 2 W. If heat transfer coefficient on both surfaces of the plate is stated to be 87.5 W/m2K, workout the reflectivity of the platea)0.35b)0.45c)0.55d)0.65Correct answer is option 'B'. Can you explain this answer?
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A thin metal plate of 4 cm diameter is suspended in atmospheric air whose temperature is 290 K. This plate attains a temperature of 295 K when one of its face receives radiant energy from a heat source at the rate of 2 W. If heat transfer coefficient on both surfaces of the plate is stated to be 87.5 W/m2K, workout the reflectivity of the platea)0.35b)0.45c)0.55d)0.65Correct answer is option 'B'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about A thin metal plate of 4 cm diameter is suspended in atmospheric air whose temperature is 290 K. This plate attains a temperature of 295 K when one of its face receives radiant energy from a heat source at the rate of 2 W. If heat transfer coefficient on both surfaces of the plate is stated to be 87.5 W/m2K, workout the reflectivity of the platea)0.35b)0.45c)0.55d)0.65Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thin metal plate of 4 cm diameter is suspended in atmospheric air whose temperature is 290 K. This plate attains a temperature of 295 K when one of its face receives radiant energy from a heat source at the rate of 2 W. If heat transfer coefficient on both surfaces of the plate is stated to be 87.5 W/m2K, workout the reflectivity of the platea)0.35b)0.45c)0.55d)0.65Correct answer is option 'B'. Can you explain this answer?.
A thin metal plate of 4 cm diameter is suspended in atmospheric air whose temperature is 290 K. This plate attains a temperature of 295 K when one of its face receives radiant energy from a heat source at the rate of 2 W. If heat transfer coefficient on both surfaces of the plate is stated to be 87.5 W/m2K, workout the reflectivity of the platea)0.35b)0.45c)0.55d)0.65Correct answer is option 'B'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about A thin metal plate of 4 cm diameter is suspended in atmospheric air whose temperature is 290 K. This plate attains a temperature of 295 K when one of its face receives radiant energy from a heat source at the rate of 2 W. If heat transfer coefficient on both surfaces of the plate is stated to be 87.5 W/m2K, workout the reflectivity of the platea)0.35b)0.45c)0.55d)0.65Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thin metal plate of 4 cm diameter is suspended in atmospheric air whose temperature is 290 K. This plate attains a temperature of 295 K when one of its face receives radiant energy from a heat source at the rate of 2 W. If heat transfer coefficient on both surfaces of the plate is stated to be 87.5 W/m2K, workout the reflectivity of the platea)0.35b)0.45c)0.55d)0.65Correct answer is option 'B'. Can you explain this answer?.
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