Control volume T dE dt Bulb sensor т, су T(t) The bulb thermometer shown initially reads 42 degrees Celsius. Then, it is instantly exposed to an external temperature of 96 degrees Celsius. How long will it take for the reading to show 98% of the step change? The time constant is given as 7.6 seconds. (Hint: 98% of step change is: 42+0.98*(96-42))
Control volume T dE dt Bulb sensor т, су T(t) The bulb thermometer shown initially reads 42 degrees Celsius. Then, it is instantly exposed to an external temperature of 96 degrees Celsius. How long will it take for the reading to show 98% of the step change? The time constant is given as 7.6 seconds. (Hint: 98% of step change is: 42+0.98*(96-42))
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![### Thermodynamics of a Bulb Thermometer
#### Diagram Explanation:
The diagram illustrates a bulb thermometer with a focus on its thermal properties:
- **Control Volume:** Illustrated as a dashed line enclosing the bulb sensor.
- **Bulb Sensor:** The highlighted area where temperature measurements occur.
- **Variables and Parameters:**
- \( T_o \): External temperature.
- \( \frac{dE}{dt} \): Rate of change of energy within the control volume.
- \( m, c_v, T(t) \): Mass, specific heat capacity, and temperature as a function of time for the bulb sensor.
- \( \dot{Q}_{\text{in}} \): Heat transfer rate into the system.
#### Problem Statement:
The bulb thermometer initially registers a temperature of 42 degrees Celsius. It is then exposed to an external temperature of 96 degrees Celsius. The task is to determine how long it will take for the thermometer reading to reflect 98% of the step change. The time constant of the system is given as 7.6 seconds.
**Hint for Calculation:**
The formula to find 98% of the step change is:
\[ 42 + 0.98 \times (96 - 42) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c68f49e-68dd-4957-98f9-2eef30804977%2F2c94dc0e-9466-44cc-a106-42e33847c32f%2F9kdto98_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Thermodynamics of a Bulb Thermometer
#### Diagram Explanation:
The diagram illustrates a bulb thermometer with a focus on its thermal properties:
- **Control Volume:** Illustrated as a dashed line enclosing the bulb sensor.
- **Bulb Sensor:** The highlighted area where temperature measurements occur.
- **Variables and Parameters:**
- \( T_o \): External temperature.
- \( \frac{dE}{dt} \): Rate of change of energy within the control volume.
- \( m, c_v, T(t) \): Mass, specific heat capacity, and temperature as a function of time for the bulb sensor.
- \( \dot{Q}_{\text{in}} \): Heat transfer rate into the system.
#### Problem Statement:
The bulb thermometer initially registers a temperature of 42 degrees Celsius. It is then exposed to an external temperature of 96 degrees Celsius. The task is to determine how long it will take for the thermometer reading to reflect 98% of the step change. The time constant of the system is given as 7.6 seconds.
**Hint for Calculation:**
The formula to find 98% of the step change is:
\[ 42 + 0.98 \times (96 - 42) \]
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