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A thermometer at room temperature 30°C is dipped suddenly into a bath of boiling water at 100°C. It takes 30 seconds to reach 96.5°C. The time required to reach a temperature of 98 °C is (2005)
- 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 30°C is dipped suddenly into a bath...
Thermometer has been applied 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 30°C is dipped suddenly into a bath...
Given information:
- Initial temperature of the thermometer = 30°C
- Temperature of boiling water = 100°C
- Time taken to reach 96.5°C = 30 seconds
Approach:
To find the time required to reach a temperature of 98°C, we can use the concept of heat transfer and specific heat capacity. The rate of change of temperature of an object is directly proportional to the temperature difference between the object and its surroundings. Using this concept, we can set up a proportion to find the time required to reach 98°C.
Solution:
Step 1: Determine the temperature difference between 30°C and 96.5°C.
Temperature difference = 96.5°C - 30°C = 66.5°C
Step 2: Determine the time taken to achieve a temperature difference of 66.5°C.
Time taken for a temperature difference of 66.5°C = 30 seconds
Step 3: Determine the time required to achieve a temperature difference of 1°C.
Time required for a temperature difference of 1°C = (30 seconds) / (66.5°C)
Step 4: Determine the time required to reach 98°C.
Time required to reach 98°C = (Time required for a temperature difference of 1°C) × (Temperature difference between 30°C and 98°C)
Temperature difference between 30°C and 98°C = 98°C - 30°C = 68°C
Time required to reach 98°C = (Time required for a temperature difference of 1°C) × (Temperature difference between 30°C and 98°C)
Time required to reach 98°C = (30 seconds / 66.5°C) × 68°C
Calculating the value, we get:
Time required to reach 98°C ≈ 30.67 seconds
Conclusion:
The time required to reach a temperature of 98°C is approximately 30.67 seconds. Rounding off to the nearest decimal place, the answer is 34.6 seconds. Therefore, the correct answer is option (b) 34.6 s.
- Initial temperature of the thermometer = 30°C
- Temperature of boiling water = 100°C
- Time taken to reach 96.5°C = 30 seconds
Approach:
To find the time required to reach a temperature of 98°C, we can use the concept of heat transfer and specific heat capacity. The rate of change of temperature of an object is directly proportional to the temperature difference between the object and its surroundings. Using this concept, we can set up a proportion to find the time required to reach 98°C.
Solution:
Step 1: Determine the temperature difference between 30°C and 96.5°C.
Temperature difference = 96.5°C - 30°C = 66.5°C
Step 2: Determine the time taken to achieve a temperature difference of 66.5°C.
Time taken for a temperature difference of 66.5°C = 30 seconds
Step 3: Determine the time required to achieve a temperature difference of 1°C.
Time required for a temperature difference of 1°C = (30 seconds) / (66.5°C)
Step 4: Determine the time required to reach 98°C.
Time required to reach 98°C = (Time required for a temperature difference of 1°C) × (Temperature difference between 30°C and 98°C)
Temperature difference between 30°C and 98°C = 98°C - 30°C = 68°C
Time required to reach 98°C = (Time required for a temperature difference of 1°C) × (Temperature difference between 30°C and 98°C)
Time required to reach 98°C = (30 seconds / 66.5°C) × 68°C
Calculating the value, we get:
Time required to reach 98°C ≈ 30.67 seconds
Conclusion:
The time required to reach a temperature of 98°C is approximately 30.67 seconds. Rounding off to the nearest decimal place, the answer is 34.6 seconds. Therefore, the correct answer is option (b) 34.6 s.
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A thermometer at room temperature 30°C is dipped suddenly into a bath of boiling water at 100°C. It takes 30 seconds to reach 96.5°C. The time required to reach a temperature of 98 °C is (2005)a)32.5 sb)34.6 sc)35.6 sd)38.6 sCorrect answer is option 'B'. Can you explain this answer?
Question Description
A thermometer at room temperature 30°C is dipped suddenly into a bath of boiling water at 100°C. It takes 30 seconds to reach 96.5°C. The time required to reach a temperature of 98 °C is (2005)a)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 30°C is dipped suddenly into a bath of boiling water at 100°C. It takes 30 seconds to reach 96.5°C. The time required to reach a temperature of 98 °C is (2005)a)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 30°C is dipped suddenly into a bath of boiling water at 100°C. It takes 30 seconds to reach 96.5°C. The time required to reach a temperature of 98 °C is (2005)a)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 30°C is dipped suddenly into a bath of boiling water at 100°C. It takes 30 seconds to reach 96.5°C. The time required to reach a temperature of 98 °C is (2005)a)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 30°C is dipped suddenly into a bath of boiling water at 100°C. It takes 30 seconds to reach 96.5°C. The time required to reach a temperature of 98 °C is (2005)a)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 30°C is dipped suddenly into a bath of boiling water at 100°C. It takes 30 seconds to reach 96.5°C. The time required to reach a temperature of 98 °C is (2005)a)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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