27% of heat produced by the stove's gas burner is transferred to the soup in the covered pot, the rest is lost. Determine the total mass in grams of methane that must be burned to heat 800 ml of water from 22 to 90 degrees C. The density is 1.08 g/ml and the specific heat is 4.06 j/g degree C.
I'm not sure how to go about answering this question
To solve this problem, you need to calculate the amount of heat required to raise the temperature of the water from 22 to 90 degrees Celsius, and then use the given efficiency to determine the total heat produced by burning methane. Finally, you can calculate the mass of methane required.
Step 1: Calculate the heat required to raise the temperature of the water:
Heat = mass x specific heat x temperature change
Given:
Specific heat (c) = 4.06 j/g degree C
Temperature change (ΔT) = 90 - 22 = 68 degrees Celsius
Volume of water (V) = 800 ml
Density of water = 1.08 g/ml
First, convert the volume of water to grams:
Mass = Density x Volume
Mass = 1.08 g/ml x 800 ml
Step 2: Calculate the heat energy required:
Heat = mass x specific heat x temperature change
Step 3: Determine the total heat produced:
From the given information, we know that only 27% (0.27) of the heat produced by burning methane is transferred to the soup. This means the rest is lost.
Total heat produced = Heat / 0.27
Step 4: Calculate the mass of methane burned:
We know that for every mole of methane (CH4), 890 kJ of energy is released (heat of combustion). We can use this information to relate the heat produced to the mass of methane burned.
1 mole of CH4 = 16 g
890 kJ = 1 mole of CH4
Mass of CH4 = 890 kJ x (Total heat produced / 1 mole CH4) x (mass of 1 mole CH4 / 16 g)
Now you can plug in the values and solve for the mass of methane burned.