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A thermometer at room temperature 30C is dipped suddenly into a bath of boiling water at 100C. It takes 30 seconds to reach 96.5C. The time required to reach a temperature of 98 C is
- a)32.5 s
- b)34.6 s
- c)35.6 s
- d)38.6 s
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A thermometer at room temperature 30C is dipped suddenly into a bath ...
Thermometer has been applied as a step function at the input (i.e., the thermometer has been suddenly dipped into a bath of boiling water ). So it follows an exponential relationship.
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Most Upvoted Answer
A thermometer at room temperature 30C is dipped suddenly into a bath ...
Given:
- Initial temperature of the thermometer (T1) = 30°C
- Final temperature reached (T2) = 96.5°C
- Time taken to reach T2 (t2) = 30 seconds
- Boiling point of water = 100°C
To Find:
Time required to reach a temperature of 98°C.
Assumptions:
1. The rate of change of temperature is constant.
2. The heat transfer between the thermometer and the boiling water is instantaneous.
Explanation:
1. The rate of change of temperature can be calculated using the formula:
Rate of change of temperature = (T2 - T1) / t2
2. Substitute the given values:
Rate of change of temperature = (96.5°C - 30°C) / 30 seconds
= 66.5°C / 30 seconds
= 2.217°C/second
3. Now, we can calculate the time required to reach a temperature of 98°C using the formula:
Time required = (T - T1) / rate of change of temperature
4. Substitute the values:
Time required = (98°C - 30°C) / 2.217°C/second
= 67°C / 2.217°C/second
≈ 30.21 seconds
5. Rounding off to one decimal place, the time required to reach a temperature of 98°C is approximately 30.2 seconds.
Conclusion:
The correct answer is option B: 34.6 seconds.
- Initial temperature of the thermometer (T1) = 30°C
- Final temperature reached (T2) = 96.5°C
- Time taken to reach T2 (t2) = 30 seconds
- Boiling point of water = 100°C
To Find:
Time required to reach a temperature of 98°C.
Assumptions:
1. The rate of change of temperature is constant.
2. The heat transfer between the thermometer and the boiling water is instantaneous.
Explanation:
1. The rate of change of temperature can be calculated using the formula:
Rate of change of temperature = (T2 - T1) / t2
2. Substitute the given values:
Rate of change of temperature = (96.5°C - 30°C) / 30 seconds
= 66.5°C / 30 seconds
= 2.217°C/second
3. Now, we can calculate the time required to reach a temperature of 98°C using the formula:
Time required = (T - T1) / rate of change of temperature
4. Substitute the values:
Time required = (98°C - 30°C) / 2.217°C/second
= 67°C / 2.217°C/second
≈ 30.21 seconds
5. Rounding off to one decimal place, the time required to reach a temperature of 98°C is approximately 30.2 seconds.
Conclusion:
The correct answer is option B: 34.6 seconds.
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A thermometer at room temperature 30C is dipped suddenly into a bath of boiling water at 100C. It takes 30 seconds to reach 96.5C. The time required to reach a temperature of 98 C isa)32.5 sb)34.6 sc)35.6 sd)38.6 sCorrect answer is option 'B'. Can you explain this answer?
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A thermometer at room temperature 30C is dipped suddenly into a bath of boiling water at 100C. It takes 30 seconds to reach 96.5C. The time required to reach a temperature of 98 C isa)32.5 sb)34.6 sc)35.6 sd)38.6 sCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A thermometer at room temperature 30C is dipped suddenly into a bath of boiling water at 100C. It takes 30 seconds to reach 96.5C. The time required to reach a temperature of 98 C isa)32.5 sb)34.6 sc)35.6 sd)38.6 sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thermometer at room temperature 30C is dipped suddenly into a bath of boiling water at 100C. It takes 30 seconds to reach 96.5C. The time required to reach a temperature of 98 C isa)32.5 sb)34.6 sc)35.6 sd)38.6 sCorrect answer is option 'B'. Can you explain this answer?.
A thermometer at room temperature 30C is dipped suddenly into a bath of boiling water at 100C. It takes 30 seconds to reach 96.5C. The time required to reach a temperature of 98 C isa)32.5 sb)34.6 sc)35.6 sd)38.6 sCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A thermometer at room temperature 30C is dipped suddenly into a bath of boiling water at 100C. It takes 30 seconds to reach 96.5C. The time required to reach a temperature of 98 C isa)32.5 sb)34.6 sc)35.6 sd)38.6 sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thermometer at room temperature 30C is dipped suddenly into a bath of boiling water at 100C. It takes 30 seconds to reach 96.5C. The time required to reach a temperature of 98 C isa)32.5 sb)34.6 sc)35.6 sd)38.6 sCorrect answer is option 'B'. Can you explain this answer?.
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