Boiling Water at High Pressure. When water is boiled at a...

Boiling Water at High Pressure. When water is boiled at a pressure of 2.00 atm, the heat of vaporization is $2.20 \times 10^{6} \mathrm{J} / \mathrm{kg}$ and the boiling point is $120^{\circ} \mathrm{C}$ . At this pressure, 1.00 $\mathrm{kg}$ of water has a volume of $1.00 \times 10^{-3} \mathrm{m}^{3},$ and 1.00 $\mathrm{kg}$ of steam has a volume of 0.824 $\mathrm{m}^{3} .$ (a) Compute the work done when 1.00 $\mathrm{kg}$ of steam is formed at this temperature. (b) Compute the increase in internal energy of the water.

Key Concepts

Phase Change and Latent Heat

Phase change refers to the transition of a substance from one state of matter to another, such as from liquid to gas, without a change in temperature. Latent heat is the energy absorbed or released during this transition, which allows the substance to overcome intermolecular forces rather than increasing kinetic energy. This concept is central to understanding how energy is managed during boiling and condensation processes.

Work in Thermodynamic Processes

Work in a thermodynamic context is the energy transferred when a system undergoes a volume change under pressure. When a substance like water vaporizes, its volume increases dramatically and, if the process occurs at constant pressure, the work done by the system can be calculated using the product of the pressure and the change in volume. This principle is fundamental in analyzing energy exchanges during expansion or compression in various thermodynamic processes.

First Law of Thermodynamics

The First Law of Thermodynamics is a statement of energy conservation, asserting that the change in a system’s internal energy is equal to the heat supplied to the system minus the work done by the system on its surroundings. This law provides a framework for understanding how energy is distributed during processes such as boiling, where energy is used both to change the phase of the substance and to perform work against external pressure.

Transcript

00:01 So here we are given water that is being boiled at the cost of pressure of two atmospheres and at the temperature of 120 degrees celsius.

00:13 Since it is boiled at the cost of temperature, when water changes from liquid state to steam state, to the gas state, it changes its volume, of course, its volume is rapidly increasing.

00:27 And this increase in volume, which is given in the problem from initial volume, we 1 to final volume, we do.

00:38 This change in volume is corresponding to certain work done.

00:42 So for the party of this solution, we need to evaluate this work that is being done while the water is being evaporated.

00:52 So for the total heat of vaporization, the heat of vaporization was given also in the problem, the work done to uprise the water will be the work done.

01:08 And here we can use a standard formula for constant pressure work.

01:14 So at a constant pressure p, the work will be only related to the change of volumes.

01:23 So here we can immediately substitute the known values.

01:28 So this is going to be 2 times 1 .013.

01:33 This is a conversion.

01:34 From atmospheres to skulls times the change is going to be from 0 .8 to 4 meters cubes minus 1 times 10 to the minus 3 meters cubed and this will finally give us work that equals 1 .76 sorry times 10 to the 5th degree jules.

02:08 So here we know the work done for the vaporization of the water...

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