# Heat, harmonics, power, calories, efficiency, velocity, wave

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1. If you compare the temperature that water boils at sea level and at 5000 feet, what is true?

2. The frequency of the second harmonic of a wave is 1000hz. What is the frequency of the third harmonic ?

3. water flows over a waterfall 10m to a turbine. Water flows at a rate of 10kg/sec. How much power is delivered to the turbine?

4. How many calories per second is generated by the turbine?

5. Water flows over a waterfall into a turbine as the above. The turbine is connected to a generator that generates electricity that runs a heater that heats 100 grams of water. How long does it take to raise the temperature of the water 4 degrees C?

There are no losses of any kind . How long does it take to raise the water in the cup to 4 degrees C?

6. A gasoline engine fuel burns at a temperature of 500 degrees C. its radiator cools to 70 degrees C. What is the engine's Carnot efficiency?

7. A 1.25 meter long wire has a mass of 150 grams. The wire is stretched with a force of 2 newtons. What is the velocity of a wave along the wire?

8. Concrete has a specific heat capacity of 670 joules/kg-degrees C. A 2kg concrete block, that has a temperature of 20 degrees C, is dropped from a height of 100 meters. What is its temperature after it hits the ground if it lost no heat to the surrounding environment?

9. Referring to the above problem, the block is now raised back to 100 meters with out losing or gaining heat from the environment. What is the blocks temperature after it was raised?

a. Less than it was after it fell

b. This can't be determined

c. 20 degrees C, the same as it was before it fell

10. Waves travel 5000m/s along a wire that is 2m long. What is the wave length of its first harmonic?

11. What is the frequency of the first harmonic?

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#### Solution Preview

Please refer to the attachment.

1. If you compare the temperature that water boils at sea level and at 5000 feet, what is true?

Answer: Boiling temperature of a liquid depends upon the air pressure on its surface; lower the pressure lower the boiling temperature. At 5000 feet, the air pressure is lower than that at sea level. Hence, boiling temperature at 5000 ft is lower than that at sea level.

2. The frequency of the second harmonic of a wave is 1000 Hz. What is the frequency of the third harmonic?

Answer: Second harmonic wave has a frequency double the fundamental frequency. Hence, fundamental frequency is 1000/2 = 500 Hz. Third harmonic has a frequency three times the fundamental frequency. Hence, third harmonic has a frequency 3 x 500 = 1500 Hz.

3. Water flows over a waterfall 10m to a turbine. Water flows at a rate of 10kg/sec. How much power is delivered to the turbine?

Answer: Water flowing per sec. = m = 10 kg, Height = h = 10 m.

Power delivered to the turbine = Potential energy of water ...

#### Solution Summary

Heat, harmonics, power, calories, efficiency, velocity, and waves are examined.