Question

We showed that you need to expend 8,340 Btu to heat up 20 gallons of water from room temperature at 70F to 120F to produce hot water to take a shower. From this we calculated the amount of natural gas that you would burn to heat 20 gallons of water from room temperature at 70F to 120F to take a shower is 8.34 ft^3. Determine the additional amount of gas that must be burned if the water heater has an efficiency of (a) 80 percent, (b) 85 percent, and (c) 90 percent.

Efficiency = desired output/required output

Answer 1

a)

x=amount of water for 80 percent efficiency

0.8=(20/x)

x=25 gallons of water

8.34ft^3 of gas for 20 gallons

how much is required for 25 gallons

p1=(8.34*25/20)=10.425 ft^3 of gas is required for 80 percent efficiency.

Additional amount=10.425-8.34=2.085 ft^3

b)

y=amount of water for 85 percent efficiency

0.85=(20/y)

y= 23.53 gallons of water

8.34ft^3 of gas for 20 gallons

how much is required for 23.53 gallons

p2=(8.34*23.53/20)=9.812 ft^3 of gas is required for 80 percent efficiency.

Additional amount=9.812-8.34=1.472 ft^3

c)

z=amount of water for 90 percent efficiency

0.9=(20/z)

z=22.22 gallons of water

8.34ft^3 of gas for 20 gallons

how much is required for 22.22 gallons

p3=(8.34*22.22/20)=9.267 ft^3 of gas is required for 80 percent efficiency.

Additional amount=9.267-8.34=0.927 ft^3