UPSC Exam > UPSC Questions > A furnace having inside temperature of 2250 °...
Start Learning for Free
A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiation
a) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W?
a) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W?
Most Upvoted Answer
A furnace having inside temperature of 2250 °C has a glass circular vi...
To calculate the heat loss from the glass window of the furnace due to radiation, we can use the Stefan-Boltzmann law. The formula for heat loss through radiation is given by:
Heat Loss (Q)
Q = A × ε × σ × (T₁^4 - T₂^4)
Where:
- A = Area of the glass window (m²)
- ε = Emissivity of the glass (1 - transmissivity)
- σ = Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²K⁴)
- T₁ = Inside temperature (K)
- T₂ = Outside temperature (K, assumed to be 25 °C, or 298 K)
Step 1: Calculate Area (A)
- Diameter of the glass = 6 cm = 0.06 m
- Radius (r) = 0.03 m
- A = πr² = π(0.03)² ≈ 0.002827 m²
Step 2: Calculate Emissivity (ε)
- Transmissivity = 0.08
- ε = 1 - Transmissivity = 1 - 0.08 = 0.92
Step 3: Convert Temperatures to Kelvin
- T₁ = 2250 °C = 2250 + 273.15 = 2523.15 K
- T₂ = 25 °C = 25 + 273.15 = 298.15 K
Step 4: Calculate Heat Loss (Q)
Using the Stefan-Boltzmann law:
Q = 0.002827 × 0.92 × 5.67 × 10⁻⁸ × (2523.15^4 - 298.15^4)
Calculating the temperature differences:
- T₁^4 ≈ 4.058 × 10¹³ K⁴
- T₂^4 ≈ 6.379 × 10¹⁰ K⁴
Now substituting the values:
Q ≈ 0.002827 × 0.92 × 5.67 × 10⁻⁸ × (4.058 × 10¹³ - 6.379 × 10¹⁰)
Calculating gives:
Q ≈ 652.32 W
Final Result
The heat loss from the glass window due to radiation is approximately 652.32 W. Thus, the correct answer is (b) 652.32 W.
Heat Loss (Q)
Q = A × ε × σ × (T₁^4 - T₂^4)
Where:
- A = Area of the glass window (m²)
- ε = Emissivity of the glass (1 - transmissivity)
- σ = Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²K⁴)
- T₁ = Inside temperature (K)
- T₂ = Outside temperature (K, assumed to be 25 °C, or 298 K)
Step 1: Calculate Area (A)
- Diameter of the glass = 6 cm = 0.06 m
- Radius (r) = 0.03 m
- A = πr² = π(0.03)² ≈ 0.002827 m²
Step 2: Calculate Emissivity (ε)
- Transmissivity = 0.08
- ε = 1 - Transmissivity = 1 - 0.08 = 0.92
Step 3: Convert Temperatures to Kelvin
- T₁ = 2250 °C = 2250 + 273.15 = 2523.15 K
- T₂ = 25 °C = 25 + 273.15 = 298.15 K
Step 4: Calculate Heat Loss (Q)
Using the Stefan-Boltzmann law:
Q = 0.002827 × 0.92 × 5.67 × 10⁻⁸ × (2523.15^4 - 298.15^4)
Calculating the temperature differences:
- T₁^4 ≈ 4.058 × 10¹³ K⁴
- T₂^4 ≈ 6.379 × 10¹⁰ K⁴
Now substituting the values:
Q ≈ 0.002827 × 0.92 × 5.67 × 10⁻⁸ × (4.058 × 10¹³ - 6.379 × 10¹⁰)
Calculating gives:
Q ≈ 652.32 W
Final Result
The heat loss from the glass window due to radiation is approximately 652.32 W. Thus, the correct answer is (b) 652.32 W.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W?
Question Description
A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W?.
A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W?.
Solutions for A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W? defined & explained in the simplest way possible. Besides giving the explanation of
A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W?, a detailed solution for A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W? has been provided alongside types of A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W? theory, EduRev gives you an
ample number of questions to practice A furnace having inside temperature of 2250 °C has a glass circular viewing of 6 cm diameter. If the transmissivity of glass is 0.08, make calculations for the heat loss from the glass window due to radiationa) 234.54 W c) 328.53 W b) 652.32 W d) 762.32 W? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup