A 2.75 kg block of ice is heated until it completely melts. It is then heated again until it completely changes to water vapor. Is more energy required to melt the ice or to vaporize the liquid water.
q1 to melt ice = mass ice x heat fusion.
q2 to raise T to 100 C = mass H2O x specific heat H2O x (Tfinal-Tinitial)
q2* to torn liquid H2O at 100 C to steam at 100 C = mass H2O x heat vaporization.
Total to melt ice = q1
Total to raise T from zero to 100 and turn steam is q2 + q2*
Compare q1 to (sum q2+q2*)
Note: The question is somewhat misleading. I assume the question means to heat the H2O from zero C to 100 C and continue heating until the liquid changes to vapor. But water has an appreciable vapor pressure at say room temperature and will vaporize completely if we wait long enough. The heat required to vaporize H2O at 25C is not the same as the sum of q2 and q2* above.
Well, let's break the ice on this question! When you melt ice, you need to heat it up from its freezing point (0 degrees Celsius) to its melting point (also 0 degrees Celsius). This process requires a certain amount of energy, known as the heat of fusion. However, when you want to turn liquid water into water vapor, you need to continue heating it above its boiling point (100 degrees Celsius). This process requires even more energy, known as the heat of vaporization. So, between the two, more energy is required to vaporize the liquid water. It's like going from being shy (ice) to being a total steam machine (water vapor) takes some extra oomph!
More energy is required to vaporize the liquid water than to melt the ice.
The process of melting ice requires energy to break the intermolecular bonds holding the ice molecules together. This is known as the heat of fusion. The heat of fusion for ice is approximately 334 kJ/kg. So, for a 2.75 kg block of ice, the total energy required to melt it completely would be 2.75 kg * 334 kJ/kg = 918.5 kJ.
Once the ice has melted and turned into liquid water, further energy is needed to convert the liquid water into water vapor. This process is called vaporization or evaporation. The energy required to vaporize liquid water is known as the heat of vaporization. The heat of vaporization for water is about 2260 kJ/kg. Hence, the total energy required to completely vaporize the liquid water obtained from the melted ice would be 2.75 kg * 2260 kJ/kg = 6215 kJ.
Therefore, it takes more energy to vaporize the liquid water compared to melting the ice.
To determine whether more energy is required to melt the ice or to vaporize the liquid water, we can analyze the specific heat capacities and latent heats of fusion and vaporization.
The specific heat capacity (c) is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius per unit mass.
For ice, the specific heat capacity is approximately 2.09 J/g°C, which means that it takes 2.09 Joules of energy to raise the temperature of 1 gram of ice by 1 degree Celsius. However, in this case, we are not concerned about temperature change but rather phase change.
Latent heat is the amount of heat energy required to undergo a phase change without a change in temperature. There are two types of latent heat: latent heat of fusion and latent heat of vaporization.
The latent heat of fusion (Lf) is the amount of heat energy required to convert a solid into a liquid at its melting point. For water, the value of Lf is approximately 334 J/g.
The latent heat of vaporization (Lv) is the amount of heat energy required to convert a liquid into a gas at its boiling point. For water, the value of Lv is approximately 2260 J/g.
To determine the energy required to melt the ice, we can use the formula:
Energy = mass x latent heat of fusion
In this case:
Energy (to melt ice) = 2.75 kg x 334 J/g = 918.5 kJ
To determine the energy required to vaporize the liquid water, we can use the formula:
Energy = mass x latent heat of vaporization
Since the ice has completely melted and turned into liquid water, the mass remains unchanged at 2.75 kg.
Energy (to vaporize water) = 2.75 kg x 2260 J/g = 6215 kJ
As we can see, the energy required to vaporize the liquid water is significantly larger than the energy required to melt the ice. Therefore, more energy is required to vaporize the liquid water than to melt the ice.