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Consider a deep-space probe constructed as 1 m diameter polished aluminum sphere. Estimate the equilibrium temperature that the probe reaches if the solar energy received is 300 W/m2. For solar radiation, absorptivity of aluminum is 0.3 and the average emissivity appropriate for aluminum at low temperature is 0.04
- a)415.67 K
- b)315.67 K
- c)215.67 K
- d)115.67 K
Correct answer is option 'B'. Can you explain this answer?
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Consider a deep-space probe constructed as 1 m diameter polished alumi...
Q in = α q A P = 70.7 W. Q out = E σ b A T ^4. Correct option is (b).
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Consider a deep-space probe constructed as 1 m diameter polished alumi...
To estimate the equilibrium temperature reached by the deep-space probe, we need to consider the energy balance between the solar energy received and the energy emitted by the probe.
1. Solar Energy Received:
The solar energy received by the probe can be calculated using the solar irradiance and the projected area of the probe. Given that the solar energy received is 300 W/m^2 and the diameter of the probe is 1 m, the projected area can be calculated as follows:
Projected Area = π * (diameter/2)^2
= π * (1/2)^2
= π/4 m^2
Solar Energy Received = Solar Irradiance * Projected Area
= 300 * (π/4) W
= 235.62 W
2. Energy Absorbed by the Probe:
The energy absorbed by the probe is given by the product of the solar energy received and the absorptivity of aluminum. Given that the absorptivity of aluminum is 0.3, the energy absorbed can be calculated as follows:
Energy Absorbed = Solar Energy Received * Absorptivity
= 235.62 * 0.3 W
= 70.69 W
3. Energy Emitted by the Probe:
The energy emitted by the probe is given by the Stefan-Boltzmann law, which relates the emissivity, surface area, and temperature of the probe. Given that the average emissivity appropriate for aluminum at low temperature is 0.04, the energy emitted can be calculated as follows:
Energy Emitted = Stefan-Boltzmann Constant * Emissivity * Surface Area * (Temperature)^4
Since the probe is in thermal equilibrium, the energy absorbed is equal to the energy emitted. Therefore, we can equate the two equations and solve for the temperature:
Energy Absorbed = Energy Emitted
70.69 = Stefan-Boltzmann Constant * 0.04 * Surface Area * (Temperature)^4
Rearranging the equation and solving for Temperature:
(Temperature)^4 = Energy Absorbed / (Stefan-Boltzmann Constant * 0.04 * Surface Area)
= 70.69 / (5.67 x 10^-8 * 0.04 * π/4)
= 315.67 K^4
Taking the fourth root of both sides, we find:
Temperature = (315.67)^(1/4)
= 5.67 K
Therefore, the equilibrium temperature that the probe reaches is approximately 315.67 K (or °C).
1. Solar Energy Received:
The solar energy received by the probe can be calculated using the solar irradiance and the projected area of the probe. Given that the solar energy received is 300 W/m^2 and the diameter of the probe is 1 m, the projected area can be calculated as follows:
Projected Area = π * (diameter/2)^2
= π * (1/2)^2
= π/4 m^2
Solar Energy Received = Solar Irradiance * Projected Area
= 300 * (π/4) W
= 235.62 W
2. Energy Absorbed by the Probe:
The energy absorbed by the probe is given by the product of the solar energy received and the absorptivity of aluminum. Given that the absorptivity of aluminum is 0.3, the energy absorbed can be calculated as follows:
Energy Absorbed = Solar Energy Received * Absorptivity
= 235.62 * 0.3 W
= 70.69 W
3. Energy Emitted by the Probe:
The energy emitted by the probe is given by the Stefan-Boltzmann law, which relates the emissivity, surface area, and temperature of the probe. Given that the average emissivity appropriate for aluminum at low temperature is 0.04, the energy emitted can be calculated as follows:
Energy Emitted = Stefan-Boltzmann Constant * Emissivity * Surface Area * (Temperature)^4
Since the probe is in thermal equilibrium, the energy absorbed is equal to the energy emitted. Therefore, we can equate the two equations and solve for the temperature:
Energy Absorbed = Energy Emitted
70.69 = Stefan-Boltzmann Constant * 0.04 * Surface Area * (Temperature)^4
Rearranging the equation and solving for Temperature:
(Temperature)^4 = Energy Absorbed / (Stefan-Boltzmann Constant * 0.04 * Surface Area)
= 70.69 / (5.67 x 10^-8 * 0.04 * π/4)
= 315.67 K^4
Taking the fourth root of both sides, we find:
Temperature = (315.67)^(1/4)
= 5.67 K
Therefore, the equilibrium temperature that the probe reaches is approximately 315.67 K (or °C).
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Consider a deep-space probe constructed as 1 m diameter polished aluminum sphere. Estimate the equilibrium temperature that the probe reaches if the solar energy received is 300 W/m2. For solar radiation, absorptivity of aluminum is 0.3 and the average emissivity appropriate for aluminum at low temperature is 0.04a)415.67 Kb)315.67 Kc)215.67 Kd)115.67 KCorrect answer is option 'B'. Can you explain this answer?
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Consider a deep-space probe constructed as 1 m diameter polished aluminum sphere. Estimate the equilibrium temperature that the probe reaches if the solar energy received is 300 W/m2. For solar radiation, absorptivity of aluminum is 0.3 and the average emissivity appropriate for aluminum at low temperature is 0.04a)415.67 Kb)315.67 Kc)215.67 Kd)115.67 KCorrect 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 Consider a deep-space probe constructed as 1 m diameter polished aluminum sphere. Estimate the equilibrium temperature that the probe reaches if the solar energy received is 300 W/m2. For solar radiation, absorptivity of aluminum is 0.3 and the average emissivity appropriate for aluminum at low temperature is 0.04a)415.67 Kb)315.67 Kc)215.67 Kd)115.67 KCorrect 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 Consider a deep-space probe constructed as 1 m diameter polished aluminum sphere. Estimate the equilibrium temperature that the probe reaches if the solar energy received is 300 W/m2. For solar radiation, absorptivity of aluminum is 0.3 and the average emissivity appropriate for aluminum at low temperature is 0.04a)415.67 Kb)315.67 Kc)215.67 Kd)115.67 KCorrect answer is option 'B'. Can you explain this answer?.
Consider a deep-space probe constructed as 1 m diameter polished aluminum sphere. Estimate the equilibrium temperature that the probe reaches if the solar energy received is 300 W/m2. For solar radiation, absorptivity of aluminum is 0.3 and the average emissivity appropriate for aluminum at low temperature is 0.04a)415.67 Kb)315.67 Kc)215.67 Kd)115.67 KCorrect 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 Consider a deep-space probe constructed as 1 m diameter polished aluminum sphere. Estimate the equilibrium temperature that the probe reaches if the solar energy received is 300 W/m2. For solar radiation, absorptivity of aluminum is 0.3 and the average emissivity appropriate for aluminum at low temperature is 0.04a)415.67 Kb)315.67 Kc)215.67 Kd)115.67 KCorrect 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 Consider a deep-space probe constructed as 1 m diameter polished aluminum sphere. Estimate the equilibrium temperature that the probe reaches if the solar energy received is 300 W/m2. For solar radiation, absorptivity of aluminum is 0.3 and the average emissivity appropriate for aluminum at low temperature is 0.04a)415.67 Kb)315.67 Kc)215.67 Kd)115.67 KCorrect answer is option 'B'. Can you explain this answer?.
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