Answer:
To calculate the mass of natural gas (methane, CH4) needed to heat the water in a typical bathtub, you can use the concept of heat transfer. You'll need to consider the specific heat of water and the temperature change.
The formula to calculate the heat energy required is:
Q = mcΔT
Where:
Q = Heat energy (in joules or calories)
m = Mass (in grams)
c = Specific heat of water (in J/g°C or cal/g°C)
ΔT = Temperature change (in °C)
First, convert 95 gallons to liters (1 gallon ≈ 3.78541 liters):
Volume of water = 95 gallons × 3.78541 L/gallon ≈ 359.81795 L
Now, calculate the mass of water using its density and volume:
Density of water (ρ) = 1 g/mL = 1000 g/L
Mass of water (m) = ρ × Volume of water = 1000 g/L × 359.81795 L ≈ 359,817.95 g
The specific heat of water (c) is approximately 4.184 J/g°C.
Now, calculate the temperature change (ΔT):
ΔT = Final temperature (110°F) - Initial temperature (67°F)
ΔT = (110°F - 67°F) × 5/9 ≈ 21.67°C
Now, use the formula to calculate the heat energy (Q):
Q = mcΔT
Q = 359,817.95 g × 4.184 J/g°C × 21.67°C ≈ 31,301,829.25 J
The heat energy is in joules, but we want to find the mass of natural gas in grams. To do this, you need to convert the heat energy to mass using the energy content of methane. The energy content of methane is typically around 50 MJ/kg, which is equivalent to 50,000,000 J/kg.
Now, convert the heat energy to mass of natural gas (methane):
Mass of CH4 = Q (J) / Energy content of CH4 (J/kg)
Mass of CH4 = 31,301,829.25 J / 50,000,000 J/kg ≈ 0.626 g
So, approximately 0.626 grams of natural gas (methane) would need to be burned to heat the water in the bathtub from 67°F to 110°F.
Step-by-step explanation: