Question

Water expands when it freezes. Determine amount of work in joules, done when a system consisting of 1.0L of liquid water freezes under a constant pressure of 1.0 atm and forms 1.1L of ice.

Answer 1

Hint: The answer to this question is based on the fact that includes the calculation of work done that is given by the formula, work done$W=-P\Delta V$and by finding the change in volume, the correct answer can be deduced.

Complete step by step solution:
In the chapters of physical chemistry, we have studied the facts that are based on the equation of sublimation, freezing point depression, elevation in the boiling point and the work done for the change in one form to another form of states of matter and so on.
Let us see the calculation of work done when a system changes from one state of matter to another.
- Water in the liquid form has the fluidity and the molecules in it are moving in one particular direction and thus the liquid takes the shape of the container.
- When this liquid that is water is frozen, these water molecules take more defined shape and thus they arrange themselves crystalline structure that is six sided and thus density of this is lesser than that of the molecules in liquid
Therefore, water has more density than ice.
Now, according to the thermodynamics, work done in changing from liquid to solid with change in volume $\Delta V$ at the pressure $P$ is given by,
$W=-P\Delta V$………(1)
Now, according to the data, initial volume that is of water, ${{V}_{1}}=1.0L$
Final volume that is of ice,${{V}_{2}}=1.1L$
Thus, change in the volume, $\Delta V={{V}_{2}}-{{V}_{1}}$
\[\Rightarrow \Delta V=1.1-1.0=0.1L\]
Also, $P=1atm$
Thus, substituting these values in the equation (1), we have
\[W=-(1.0\times 0.1)=-0.1Latm\]
\[\therefore W=10.1J\]$\,\,\,\,\,\,\,\,\,$[Since, 1L atm = 101.32J)

Therefore, the correct answer is \[W=10.1J\].

Note: The negative sign that is associated with the work done indicates that the system loses energy because if the volume increases at constant pressure then the work done by the system will be negative which indicates that the system has lost energy by doing work on its surroundings.