How many grams of gasoline would you need to burn if you started with 275 gram piece of ice that started at -25C and by the end of the expirement had 100 grams of steam and the rest liquid water?
To determine how many grams of gasoline are needed to burn in order to produce the described phase transformation of ice to liquid water and steam, we need to calculate the amount of heat required at each stage. This can be done using the specific heat capacities and heat of vaporization for each substance involved.
Let's break down the problem into three steps:
1. Heating the ice from -25°C to 0°C and melting it into liquid water.
2. Heating the liquid water from 0°C to its boiling point and boiling it into steam.
3. Heating the steam from its boiling point to 100°C.
Step 1: Heating the ice and melting it
The heat required to raise the temperature of a substance can be calculated using the specific heat capacity formula:
Q = mcΔT
where:
Q = heat energy (in joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g°C)
ΔT = change in temperature (in °C)
For ice, the specific heat capacity is about 2.09 J/g°C.
Q1 = 275g × 2.09 J/g°C × (0°C - (-25°C))
= 275g × 2.09 J/g°C × 25°C
= 14,387.5 J
To convert this energy into grams of gasoline, we need to know the energy content of gasoline. On average, gasoline contains about 34.2 megajoules (MJ) per liter. Therefore, the energy content of gasoline can be converted to joules by multiplying it by 1,000,000:
Energy_content_gasoline = 34.2 MJ/L × 1,000,000 J/MJ
= 34,200,000 J/L
Now, we can calculate the grams of gasoline needed:
Grams_gasoline_step1 = Q1 / Energy_content_gasoline
Step 2: Heating the liquid water and boiling it
The specific heat capacity of liquid water is about 4.18 J/g°C. To calculate the heat required:
Q2 = 100g × 4.18 J/g°C × (100°C - 0°C)
= 418,000 J
Now, we can calculate the additional grams of gasoline needed:
Grams_gasoline_step2 = Q2 / Energy_content_gasoline
Step 3: Heating the steam
The heat required to raise the temperature of steam is calculated similarly to step 1:
Q3 = (mass of steam) × 2.03 J/g°C × (100°C - boiling point)
However, we don't know the mass of steam. We can calculate it by subtracting the mass of liquid water (100g) from the initial mass (275g):
Mass_of_steam = 275g - 100g = 175g
Now, we can calculate the heat required:
Q3 = 175g × 2.03 J/g°C × (100°C - boiling point)
Again, we can determine the grams of gasoline required:
Grams_gasoline_step3 = Q3 / Energy_content_gasoline
Finally, the total grams of gasoline needed can be found by summing up the three steps:
Total_grams_gasoline = Grams_gasoline_step1 + Grams_gasoline_step2 + Grams_gasoline_step3
Please provide the boiling point of the liquid water to complete the calculations.