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A platinum wire is used as a resistance thermometer the wire resistance was found to be 20 ohm and 36 ohm at ice point and steam point respectively and 40 ohm at melting point of antimony 630.50°C.
Find the resistance of wire of 70°C. If the resistance varies with temperature by the relation R = R0 (1 + at + b2)
Find the resistance of wire of 70°C. If the resistance varies with temperature by the relation R = R0 (1 + at + b2)
- a)31.2 ohm
- b)169.540 ohm
- c)303.540 ohm
- d)144.390 ohm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A platinum wire is used as a resistance thermometer the wire resistanc...
R = Ro (1 + at + bt2)
at ice point, t = 0
20 = R0 (1 + a x 0 + b x 0) Ro = 20
at steam point t = 1000C
36 = 20 [1 + 100 a + 104 b]
1 + 100a + 104 b = 1.8
100a + 10000 b = 0.8
at t = 630.50 C
40 = 20 [1 + 630.5a + (630.5)2b]
1 = 5.04 - 63050 b + 397530.25 b
b = - 1.2 x 10-5 a = 9.2 x 10-3 so at 700° C
R = 20 [1 + 9.2 x 10-3 x 700 - 1.2 x 10-5 (700)2]
= 31.2 ohm
Most Upvoted Answer
A platinum wire is used as a resistance thermometer the wire resistanc...
Given information:
- The resistance of platinum wire at ice point = 20 ohm
- The resistance of platinum wire at steam point = 36 ohm
- The resistance of platinum wire at melting point of antimony (630.50C) = 40 ohm
- The resistance-temperature relationship is R = R0 (1 + alpha*t)
To find: The resistance of platinum wire at 70C
Solution:
1. Calculation of alpha
- Alpha is the temperature coefficient of resistance, which is given by the formula:
alpha = (R2 - R1) / (R1 * (t2 - t1))
where,
R1 = resistance at ice point = 20 ohm
R2 = resistance at steam point = 36 ohm
t1 = temperature at ice point = 0C
t2 = temperature at steam point = 100C
Substituting the values, we get:
alpha = (36 - 20) / (20 * (100 - 0))
alpha = 0.0085 per degree Celsius
2. Calculation of resistance at 70C
- Using the resistance-temperature relationship, we can find the resistance of the wire at any temperature, provided we have the resistance at a known temperature and the value of alpha.
- Let R0 be the resistance of the wire at 0C (ice point).
- Then, the resistance at 70C can be calculated as:
R = R0 (1 + alpha*t)
where,
t = temperature in degree Celsius = 70
We need to find R. To do that, we need to find R0 first.
3. Calculation of R0
- We can use the resistance-temperature relationship at another known temperature to find R0.
- Let's use the resistance at the melting point of antimony (630.50C).
- The resistance-temperature relationship at this point is:
R = R0 (1 + alpha*t)
where,
t = temperature in degree Celsius = 630.50
Substituting the values, we get:
40 = R0 (1 + 0.0085 * 630.50)
R0 = 19.78 ohm
4. Calculation of R at 70C
- Now we can use R0 and the resistance-temperature relationship at 70C to find R.
- The resistance-temperature relationship at 70C is:
R = R0 (1 + alpha*t)
where,
t = temperature in degree Celsius = 70
Substituting the values, we get:
R = 19.78 * (1 + 0.0085 * 70)
R = 31.2 ohm
Answer: The resistance of the platinum wire at 70C is 31.2 ohm. Therefore, option (a) is correct.
- The resistance of platinum wire at ice point = 20 ohm
- The resistance of platinum wire at steam point = 36 ohm
- The resistance of platinum wire at melting point of antimony (630.50C) = 40 ohm
- The resistance-temperature relationship is R = R0 (1 + alpha*t)
To find: The resistance of platinum wire at 70C
Solution:
1. Calculation of alpha
- Alpha is the temperature coefficient of resistance, which is given by the formula:
alpha = (R2 - R1) / (R1 * (t2 - t1))
where,
R1 = resistance at ice point = 20 ohm
R2 = resistance at steam point = 36 ohm
t1 = temperature at ice point = 0C
t2 = temperature at steam point = 100C
Substituting the values, we get:
alpha = (36 - 20) / (20 * (100 - 0))
alpha = 0.0085 per degree Celsius
2. Calculation of resistance at 70C
- Using the resistance-temperature relationship, we can find the resistance of the wire at any temperature, provided we have the resistance at a known temperature and the value of alpha.
- Let R0 be the resistance of the wire at 0C (ice point).
- Then, the resistance at 70C can be calculated as:
R = R0 (1 + alpha*t)
where,
t = temperature in degree Celsius = 70
We need to find R. To do that, we need to find R0 first.
3. Calculation of R0
- We can use the resistance-temperature relationship at another known temperature to find R0.
- Let's use the resistance at the melting point of antimony (630.50C).
- The resistance-temperature relationship at this point is:
R = R0 (1 + alpha*t)
where,
t = temperature in degree Celsius = 630.50
Substituting the values, we get:
40 = R0 (1 + 0.0085 * 630.50)
R0 = 19.78 ohm
4. Calculation of R at 70C
- Now we can use R0 and the resistance-temperature relationship at 70C to find R.
- The resistance-temperature relationship at 70C is:
R = R0 (1 + alpha*t)
where,
t = temperature in degree Celsius = 70
Substituting the values, we get:
R = 19.78 * (1 + 0.0085 * 70)
R = 31.2 ohm
Answer: The resistance of the platinum wire at 70C is 31.2 ohm. Therefore, option (a) is correct.
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31.2
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A platinum wire is used as a resistance thermometer the wire resistance was found to be 20 ohm and 36 ohm at ice point and steam point respectively and 40 ohm at melting point of antimony 630.50°C.Find the resistance of wire of 70°C. If the resistance varies with temperature by the relation R = R0 (1 + at + b2)a)31.2 ohmb)169.540 ohmc)303.540 ohmd)144.390 ohmCorrect answer is option 'A'. Can you explain this answer?
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A platinum wire is used as a resistance thermometer the wire resistance was found to be 20 ohm and 36 ohm at ice point and steam point respectively and 40 ohm at melting point of antimony 630.50°C.Find the resistance of wire of 70°C. If the resistance varies with temperature by the relation R = R0 (1 + at + b2)a)31.2 ohmb)169.540 ohmc)303.540 ohmd)144.390 ohmCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A platinum wire is used as a resistance thermometer the wire resistance was found to be 20 ohm and 36 ohm at ice point and steam point respectively and 40 ohm at melting point of antimony 630.50°C.Find the resistance of wire of 70°C. If the resistance varies with temperature by the relation R = R0 (1 + at + b2)a)31.2 ohmb)169.540 ohmc)303.540 ohmd)144.390 ohmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A platinum wire is used as a resistance thermometer the wire resistance was found to be 20 ohm and 36 ohm at ice point and steam point respectively and 40 ohm at melting point of antimony 630.50°C.Find the resistance of wire of 70°C. If the resistance varies with temperature by the relation R = R0 (1 + at + b2)a)31.2 ohmb)169.540 ohmc)303.540 ohmd)144.390 ohmCorrect answer is option 'A'. Can you explain this answer?.
A platinum wire is used as a resistance thermometer the wire resistance was found to be 20 ohm and 36 ohm at ice point and steam point respectively and 40 ohm at melting point of antimony 630.50°C.Find the resistance of wire of 70°C. If the resistance varies with temperature by the relation R = R0 (1 + at + b2)a)31.2 ohmb)169.540 ohmc)303.540 ohmd)144.390 ohmCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A platinum wire is used as a resistance thermometer the wire resistance was found to be 20 ohm and 36 ohm at ice point and steam point respectively and 40 ohm at melting point of antimony 630.50°C.Find the resistance of wire of 70°C. If the resistance varies with temperature by the relation R = R0 (1 + at + b2)a)31.2 ohmb)169.540 ohmc)303.540 ohmd)144.390 ohmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A platinum wire is used as a resistance thermometer the wire resistance was found to be 20 ohm and 36 ohm at ice point and steam point respectively and 40 ohm at melting point of antimony 630.50°C.Find the resistance of wire of 70°C. If the resistance varies with temperature by the relation R = R0 (1 + at + b2)a)31.2 ohmb)169.540 ohmc)303.540 ohmd)144.390 ohmCorrect answer is option 'A'. Can you explain this answer?.
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