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What is the decrease in entropy of 25.0 g of water that condenses on a bathroom mirror at a temperature of $35.0^\circ\textrm{C}$, assuming no change in temperature and given the latent heat of vaporization to be 2450 kJ/kg?
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Final Answer

$-199 \textrm{ J/K}$

Solution Video

OpenStax College Physics Solution, Chapter 15, Problem 53 (Problems & Exercises) (1:28)

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Video Transcript

This is College Physics Answers with Shaun Dychko. Some water vapor is going to be condensing on Myer at 35 degree Celsius and the amount of water is 25 grams which is 25 times tenth to the minus three kilograms and it's going to release some heat when it condenses and the amount of heat releases is mass times the latent heat of a vaporization at 35 degrees Celsius. So the change in entropy of the water vapor is the amount of heat added to the vapor divided by its absolute temperature but heat is actually being taken out of it and so we put a minus there to indicate that So we have negative <i>mLv</i> in place of <i>Q</i> and divide that by temperature. So it’s 25 times tenth to the minus three kilograms times 2450 times tenth to the three joules per kilograms latent heat of vaporization provided by temperature of 35 degrees Celsius converted into Kelvin by adding 273.15 giving a change in entropy of negative 199 joules per Kelvin and we expected negative here because the water vapor is gone from a disorganized gaseous state into a more organized liquid state with the particles closer together. So there's an increase in the order and as a result of this change from vapor to liquid and so we expect a decrease in entropy as a result.