# Entropy change as water is frozen

## Homework Statement

A vessel containing 500 g of water, at a starting temperature of 15.0 ◦C, is placed in a freezer at −10.0 ◦C, and left to freeze. (i) If the heat capacity of the vessel is negligible, show that the total entropy change for the system of the water and the inside of the freezer, after the ice reaches the temperature of the inside of the freezer, is 31.4 J K−1 . Is this consistent with the second law of thermodynamics?

The specific heat capacities of liquid water and ice are 4190 J kg−1 K−1 and 2100 J kg−1 K−1 respectively, and its latent heat of fusion is 3.34 × 105 J kg−1 . Take the melting point of ice to be 273 K.]

## Homework Equations

$$\Delta S = mc\ln\frac{T_2}{T_1}$$
$$\Delta S = \dfrac{\Delta Q}{T}$$
$$Q= mc\Delta T$$
$$Q=ml$$

## The Attempt at a Solution

$$\Delta S_{water} = m\left[c_{water}\ln\frac{T_2}{T_1} + \frac{l}{T} + c_{ice}\ln\frac{T_2}{T_1}\right]$$ = -762.9 J K^{-1}

$$\Delta S_{surroundings} = m\frac{c_{water}\Delta T + l + c_{ice}\Delta T}{T}$$ = 751.7 J K^{-1}

I'm getting an incorrect value. What is wrong with my calculation?

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## Answers and Replies

Chestermiller
Mentor
It looks like the equations you wrote are correct. So now show us the details of the calculations.

Chet

mfb
Mentor
In particular, which numbers do you use where?