A cook wants to heat 1.10kg of water from 33 C to 100 C. If he uses the combustion of natural gas which is exothermic to heat the water, how much natural gas will he need to burn? Natural gas produces 49.3 kJ/gram.
6.8 grams
How much energy do you need to heat the water? That is q = mass x specific heat x (Tfinal-Tinitial) = 1000 x 4.184 x (100-33) = approximately 310 kJ.
CH4 + 2O2 ==> CO2 + 2H2O + 49.3 kJ/gram
1 g x 310 kJ/49.3 kJ = grams
To determine the amount of natural gas required to heat the water, we will need to calculate the amount of energy needed to raise the temperature of the water and then convert it to the equivalent amount of natural gas burned.
Step 1: Calculate the energy required to heat the water.
We can use the formula:
Energy = mass × specific heat capacity × change in temperature
The specific heat capacity of water is approximately 4.18 J/g°C.
Given:
Mass of water (m) = 1.10 kg
Initial temperature (T1) = 33 °C
Final temperature (T2) = 100 °C
Specific heat capacity of water (C) = 4.18 J/g°C
Converting mass of water to grams:
Mass of water in grams = 1.10 kg × 1000 = 1100 g
Calculating the energy required:
Energy = mass × specific heat capacity × change in temperature
Energy = 1100 g × 4.18 J/g°C × (100 °C - 33 °C)
Step 2: Convert the energy to kilojoules.
Since energy is given in joules, we need to convert it to kilojoules to match the given natural gas energy value.
1 kJ = 1000 J
Energy = (1100 g × 4.18 J/g°C × (100 °C - 33 °C)) / 1000
Step 3: Calculate the amount of natural gas burned.
We know that natural gas produces 49.3 kJ/gram.
Amount of natural gas = Energy / 49.3 kJ/gram
Substitute the calculated energy value into the formula:
Amount of natural gas = (1100 g × 4.18 J/g°C × (100 °C - 33 °C)) / (49.3 kJ/gram)
Finally, solve the equation to find the amount of natural gas required to heat the water.
To calculate the amount of natural gas needed to heat the water, we need to determine how much energy is required to heat the water from 33°C to 100°C and then convert it to the amount of natural gas needed.
1. First, we need to calculate the heat energy required to raise the temperature of the water. The heat energy can be calculated using the formula:
Q = mcΔT
Where:
Q = heat energy
m = mass of water
c = specific heat capacity of water
ΔT = change in temperature
2. The specific heat capacity of water is approximately 4.18 J/g°C. However, the mass of water is given in kilograms, so we need to convert it to grams. Thus,
Mass of water = 1.10kg × 1000g/kg = 1100g
3. Now, let's calculate the heat energy:
Q = 1100g × 4.18 J/g°C × (100°C - 33°C)
Q = 1100g × 4.18 J/g°C × 67°C
Q ≈ 311,002 J
4. Since the energy produced by natural gas is given per gram, we need to convert the heat energy from Joules to kilojoules and then divide it by the energy produced by 1 gram of natural gas:
311,002 J ÷ 1000 = 311 kJ
311 kJ ÷ 49.3 kJ/g = 6.30 g
Therefore, the cook will need to burn approximately 6.30 grams of natural gas to heat 1.10 kg of water from 33°C to 100°C.