Specific & Latent Heat

In summary: You did the problem correctly, assuming the given data is correct. You included both the heat required to raise the temperature and the heat of vaporization, which is necessary to change the state of the substance from liquid to gas. However, it is possible that your professor only wanted you to calculate the heat required to raise the temperature to the boiling point, and not the heat of vaporization. In summary, you did the problem correctly by accounting for both the increase in temperature and the change in state, but there may have been a misunderstanding of the question or a difference in what was expected from your professor.
  • #1

Homework Statement

How much heat is required to change 1.75 L of Ethyl Alcohol (C2H6O) at -50.0°C to a gas at its boiling point?

Ethyl Alcohol
V = 1.75 L
Ti = -50°C

46 g/mol
density = 0.789 g/cm3
boiling point = 78°C
specific heat (c)= 2400 J/kg*C°
Heat of Vaporization (Lv) = 850*103 J/kg

Homework Equations

density m = ρV

specific heat Q = mcΔT

latent heat Q = mLv

The Attempt at a Solution

First I determined the mass of the Ethyl Alcohol

m = ρV = (0.789 g/cm3) (1750 cm3) = 1380.75 g = 1.38075 kg

Then I solve for QNET

QNET = (mcΔT)l + mLv

QNET = [1.38 kg (2400 J/kg*C°) (78°C - (-50°C)] + [1.38 kg (850*103 J/kg)] = 1.60 * 106 J

According to the answer sheet, the answer is 4.24*105 J
What am I doing wrong?

Thank you in advance! Any and all help is appreciated!
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  • #2
The answer sheet apparently has only accounted for the heat required to raise the temperature of the liquid ethanol from -50C to 78C.
  • #3
So, did I do it correctly? It did say that "to a gas" . From my understanding of the problem as worded, I have to account for the amount of heat required to bring it to its boiling point, as well as the amount of heat required to turn it into a gas, right? Or did I do it incorrectly and I'm only suppose to calculate the amount of heat needed to bring it to the boiling point?
  • #4
Only your professor knows for sure.
  • #5

Your solution is almost correct, but there are a few errors that need to be corrected.

First, when calculating the mass of the Ethyl Alcohol, you used the volume in cm3 instead of L. This should be corrected to 1.75 L, giving a mass of 1380.75 g.

Second, in your QNET equation, you added the specific heat and latent heat terms instead of multiplying them. The correct equation should be QNET = (mcΔT) + (mLv).

Finally, when solving for QNET, you used the incorrect value for the specific heat. The specific heat for Ethyl Alcohol is actually 2.44 J/g°C, not 2400 J/kg°C. This gives a corrected value for QNET of 4.24*105 J, which matches the answer given in the solution.

Overall, your approach and equations were correct, but be sure to double check the values and units you are using to ensure accurate calculations.

1. What is specific heat?

Specific heat is the amount of heat energy required to raise the temperature of one gram of a substance by one degree Celsius.

2. How is specific heat different from latent heat?

Specific heat is the amount of heat required to change the temperature of a substance, while latent heat is the amount of heat required to change the state of a substance (i.e. from solid to liquid or liquid to gas) without changing its temperature.

3. Why is water's specific heat higher than most other substances?

Water's specific heat is higher because of its molecular structure. The hydrogen bonds between water molecules require more energy to break, making it more difficult to change the temperature of water compared to other substances.

4. What is the significance of latent heat in everyday life?

Latent heat plays a crucial role in everyday life, such as in cooking and cooling processes. For example, when water boils, it requires a large amount of heat energy to change from a liquid to a gas, which is why it takes longer to boil water than other substances with lower latent heats.

5. How is the measurement of specific and latent heat useful in scientific research?

The measurement of specific and latent heat is important in many scientific research fields, such as thermodynamics and materials science. It helps in understanding the properties and behavior of different substances and can be used to calculate energy requirements in various processes, such as in industrial applications and climate studies.

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