# Entropy change of melting ice cube initially at -5°C

• Flucky
In summary, the entropy change of an ice cube of mass 10g, at an initial temperature of -5°C, when it completely melts is 12.62 JK-1. This is calculated by adding the entropy changes from the ice going from -5°C to 0°C and from 0°C to water at 0°C. This is possible because entropy is a state function.
Flucky

## Homework Statement

Calculate the entropy change of an ice cube of mass 10g, at an initial temperature of -5°C, when it completely melts.

cice = 2.1 kJkg-1K-1
Lice-water = 3.34x105 Jkg-1

## Homework Equations

dQ = mcdT
dS = $\frac{dQ}{T}$
ΔS = $\frac{Q}{T}$
Q = mL

## The Attempt at a Solution

First I set the problem out in two stages:
a) the entropy change from the ice going from -5°C to 0°C (in order to melt)
b) the entropy change from the ice going to water

For a)
dQ = mcdT ---------(1)
dS = $\frac{dQ}{T}$ ---------(2)

Putting (1) into (2):

dS = $\frac{mcdT}{T}$
ΔS = mc∫$\frac{1}{T}$dT
ΔS = mcln(Tf/Ti)

∴ΔS1 = (0.01)(2100)ln($\frac{273}{268}$) = 0.388 JK-1

For b)
Q = mL = (0.01)(3.34x105) = 3340J

ΔS2 = $\frac{Q}{T}$ = $\frac{3340}{273}$ = 12.23 JK-1

∴ total ΔS = ΔS1 + ΔS2 = 0.388 + 12.23 = 12.62 JK-1

Am I right in simply adding the to changes of entropy together? Does ΔS work like that?

Cheers.

Looks good, and the answer is yes, the entropies add. Entropy is a state function, like gravitational potential. If you went from 0 to 1m above ground you would have g x 1m change in potential. If you went from 1m to 2m there would be a further g x 1m change in potential. Giving total change in potential = g x 2m.

Great, thanks

## What is the definition of entropy change?

Entropy change is a measure of the disorder or randomness in a system. It is a thermodynamic concept that represents the amount of energy that is unavailable for work during a process.

## What causes the entropy change of melting ice?

The entropy change of melting ice is caused by the increase in disorder of the water molecules as they transition from a solid to a liquid state. This increase in disorder leads to an increase in the system's entropy.

## How does the initial temperature of the ice cube affect its entropy change?

The initial temperature of the ice cube does not affect its entropy change. The entropy change of melting ice is only dependent on the phase change from solid to liquid, not the initial temperature of the ice.

## What is the equation for calculating the entropy change of melting ice?

The equation for calculating the entropy change of melting ice is ΔS = Q/T, where ΔS is the change in entropy, Q is the heat transfer during the phase change, and T is the temperature in Kelvin.

## How can the entropy change of melting ice be reversed?

The entropy change of melting ice can be reversed by removing heat from the liquid water and causing it to freeze back into a solid state. This process decreases the disorder of the system and decreases the entropy back to its initial state.

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