thermal power plant is generating power to supply loads through a transmission line. An electric motor is one of the loads. The efficiency of the thermal power plant is 60% and the power loss on the transmission line is 7%. If the motor’s efficiency is 95% and its output power is 100 kW, how much energy should be utilized by the power plant to feed the need of the motor for 5 hours? Choose the value that is the closest to the answer.
Question
thermal power plant is generating power to supply loads through a transmission line. An electric motor is one of the loads. The efficiency of the thermal power plant is 60% and the power loss on the transmission line is 7%. If the motor’s efficiency is 95% and its output power is 100 kW, how much energy should be utilized by the power plant to feed the need of the motor for 5 hours? Choose the value that is the closest to the answer.
Solution
To solve this problem, we need to work backwards from the motor to the power plant.
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First, we find the input power to the motor. The motor's efficiency is the ratio of output power to input power. So, the input power to the motor is output power divided by efficiency.
Input power to motor = Output power / Motor efficiency = 100 kW / 0.95 = 105.26 kW
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Next, we find the power that needs to be sent over the transmission line. The power loss on the transmission line is 7%, so the power sent over the transmission line is the input power to the motor divided by (1 - power loss percentage).
Power sent over transmission line = Input power to motor / (1 - Transmission line power loss) = 105.26 kW / (1 - 0.07) = 113.23 kW
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Finally, we find the power that needs to be generated by the power plant. The efficiency of the power plant is the ratio of output power (which is the power sent over the transmission line) to input power (which is the power generated by the power plant). So, the power generated by the power plant is the power sent over the transmission line divided by the power plant efficiency.
Power generated by power plant = Power sent over transmission line / Power plant efficiency = 113.23 kW / 0.60 = 188.72 kW
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The question asks for the energy utilized by the power plant for 5 hours. Energy is power multiplied by time, so the energy utilized by the power plant is the power generated by the power plant multiplied by the time.
Energy utilized by power plant = Power generated by power plant * Time = 188.72 kW * 5 hours = 943.6 kWh
So, the power plant needs to utilize approximately 944 kWh of energy to feed the need of the motor for 5 hours.
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