Question

What is the decrease in entropy of 25.0 g of water that condenses on a bathroom mirror at a temperature of 35.0 º C, assuming no change in temperature and given the latent heat of vaporization to be 2450 kJ/kg?

Short answer

The entropy of water is decreased by 198.86 J/K.

Step-by-step solution

Introduction

We calculate the decrease in entropy of water by finding energy released by condensation and then finding entropy change using the formula.

Change in entropy

\[\Delta S= \frac{Q}{{\bf{T}}}\]

Here,

\[\Delta S\]- change in entropy.

Q - heat transferred.

T - temperature.

 Given parameters and formula for change in entropy

Latent heat of vaporization of water 2450 kJ/kg

Mass of water = 25g = 0.025kg

Temperature T= 35 ̊ C = 308 K

 Calculate the energy released and Entropy change

Energy released

Q = mL

Q = 0.025kg × (2450 × 1000) J/kg

Q = -61250 J

Change in entropy

\begin{aligned}\Delta S= \frac{Q}{T}\\= - 61250\;{\rm{J}}/308\;{\rm{K}}\\= -198.86{\rm{J/K}} \end{aligned}

Therefore, the change in entropy is -198.86J/K.