Question

A windmill produces 1400 watts of electric power that is used to heat water. The efficiency is 100%. How long will it take to raise the temperature of 40 gallons of water by 50∘F?

Answer 1

To raise the temperature of 40 gallons of water by 50 degrees Fahrenheit using a windmill producing 1400 watts of power with 100% efficiency, it will take approximately 8.14 seconds.

Step-by-step explanation:

To determine how long it will take to raise the temperature of 40 gallons of water by 50 degrees Fahrenheit using a windmill that produces 1400 watts of electric power with 100% efficiency, we need to calculate the energy required to heat the water and then divide it by the power produced by the windmill.

The energy required to raise the temperature of the water can be calculated using the formula:

Energy = mass × specific heat capacity × change in temperature

where the mass is the volume of water converted from gallons to kilograms, the specific heat capacity of water is 4.186 J/g⋅°C, and the change in temperature is converted from Fahrenheit to Celsius.

Once we have the energy required, we can divide it by the power of the windmill to determine the time:

Time = Energy / Power

Let's plug in the values and calculate:

Volume of water = 40 gallons = 151.4 kg

Specific heat capacity of water = 4.186 J/g⋅°C

Change in temperature = 50°F - 32°F = 18°C

Energy = 151.4 kg × 4.186 J/g⋅°C × 18°C = 11,390.79 kJ

Power = 1400 watts

Time = 11,390.79 kJ / 1400 watts = 8.14 seconds

Therefore, it will take approximately 8.14 seconds to raise the temperature of 40 gallons of water by 50 degrees Fahrenheit using the given windmill.

Answer 2

3.5 h.

Step-by-step explanation:

The heat required is given by;

Q = m * Cp * dt

where,

m = mass

Cp = specific heat

dt = temperature change

Remember,

Given,

Cp = 1 Btu/(°F.lb)

1 gallon of water = 8.35 lb

m = 40 * 8.35

= 334 lb

dt = 50 °F

Q = 334 * 1 * 50

= 16700 Btu.

Converting Btu to kWh

1 kWh = 3412 Btu

1 Btu = 1/3412 kWh

16700 Btu = 16700 * 1/3412 kWh

= 4.89 kWh

Power = 1400 watts

= 1.4 kWh/h

Therefore, time required to add 4.89 kWh at a rate of 1.4kW

= 4.89/1.4

= 3.5 h.