The initial temperature of an electric machine is 30°C. When the machine is run it attains a final steady temperature of 100° C.If the heating time constant is 4 hours and the ambient temperature is 20° C, determine the temperature rise of the machine aft

Q: An electric machine's initial temperature is 30°C and reaches 100°C at steady-state. The ambient temperature is 20°C and the heating time constant is 4 hours. What is the final steady-state temperature rise?

80°C — The steady-state temperature is the final temperature - ambient temperature = 100°C - 20°C = 80°C

Q: What is the temperature rise of the machine at t = 2 hours?

47.5°C — Temperature rise is calculated using: ? = ?_ss * (1 - e^(-t/?)). ?_ss = 80°C, t = 2 hours, ? = 4 hours. ? = 80 * (1 - e^(-2/4)) = 47.5°C

Q: What is the temperature of the machine after 2 hours?

77.5°C — The machine temperature after 2 hours is the temperature rise plus the ambient temperature: 47.5°C + 30°C = 77.5°C

Q: What would be the temperature rise of the machine after 4 hours (one time constant)?

63.2°C — Using the formula ? = ?_ss * (1 - e^(-t/?)) with t=?: ? = 80 * (1 - e^(-1)) ? 63.2°C

Q: The time constant is a measure of:

How quickly the machine heats up. — The time constant defines the speed of the transient temperature response, representing the time it takes for the temperature rise to reach approximately 63.2% of its final value.

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Question 1 of 5

An electric machine's initial temperature is 30°C and reaches 100°C at steady-state. The ambient temperature is 20°C and the heating time constant is 4 hours. What is the final steady-state temperature rise?

The steady-state temperature is the final temperature - ambient temperature = 100°C - 20°C = 80°C

Question 2 of 5

What is the temperature rise of the machine at t = 2 hours?

Temperature rise is calculated using: ? = ?_ss * (1 - e^(-t/?)). ?_ss = 80°C, t = 2 hours, ? = 4 hours. ? = 80 * (1 - e^(-2/4)) = 47.5°C

Question 3 of 5

What is the temperature of the machine after 2 hours?

The machine temperature after 2 hours is the temperature rise plus the ambient temperature: 47.5°C + 30°C = 77.5°C

Question 4 of 5

What would be the temperature rise of the machine after 4 hours (one time constant)?

Using the formula ? = ?_ss * (1 - e^(-t/?)) with t=?: ? = 80 * (1 - e^(-1)) ? 63.2°C

Question 5 of 5

The time constant is a measure of:

The time constant defines the speed of the transient temperature response, representing the time it takes for the temperature rise to reach approximately 63.2% of its final value.

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