Assume you can heat water with perfect insulation (all the heat from combustion of ethanol is transferred to water). What is the volume of ethanol required to heat 100 mL of water by 10 degrees C? (You will need to look up density of ethanol, specific heat capacity or water, and heat of combustion of ethanol.)

Answer 1

To calculate the volume of ethanol required to heat 100 mL of water by 10 degrees Celsius, we will first need to find the amount of energy needed to heat water and then determine how much ethanol is needed to produce that amount of energy.

First, let's find the amount of energy needed to heat the water. We can use the formula q = mcΔT, where q is the energy (in joules), m is the mass of water (in grams), c is the specific heat capacity of water (about 4.18 J/g·C), and ΔT is the temperature difference (10 C).

The mass of 100 mL of water is approximately 100 g (since 1 mL of water has a mass of about 1 g).

So, the energy needed to heat the water is:
q = (100 g) × (4.18 J/g·C) × (10 C) = 4180 J

Now, let's find how much ethanol is needed to produce this amount of energy. We will use the heat of combustion of ethanol, which is around 29.7 kJ/g.

First, convert the energy needed to heat the water (4180 J) into kJ:
4180 J = 4.18 kJ

Now, determine the mass of ethanol needed to produce 4.18 kJ of energy:
mass of ethanol = 4.18 kJ / 29.7 kJ/g = 0.1407 g

Now, we need to convert the mass of ethanol to volume. The density of ethanol is approximately 0.789 g/mL. Using the formula density = mass/volume, we can find the volume of ethanol:

volume of ethanol = mass of ethanol / density of ethanol
volume of ethanol = 0.1407 g / 0.789 g/mL = 0.1783 mL

So, approximately 0.1783 mL of ethanol is required to heat 100 mL of water by 10 degrees Celsius with perfect insulation.