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Chapter 1: Problem 23

Is the state of the air in an isolated room completely specified by the temperature and the pressure? Explain.

Short Answer

Expert verified
Answer: No, the state of the air in an isolated room is not completely specified by the temperature and the pressure alone. Other variables like volume and the number of air particles are also needed to fully describe the state of the air.

Step by step solution

01

Investigate the variables involved in describing the state of air

The state of air in an enclosed space can be described using a number of variables. The most common of these are temperature (T), pressure (P), volume (V), and the number of air molecules or particles (n).
02

Analyze the ideal gas law

To understand the relationship between these variables, it's helpful to look at the ideal gas law, given as: PV = nRT where P is the pressure, V is the volume, n is the number of particles, R is the ideal gas constant, and T is the temperature.
03

Evaluate the importance of temperature and pressure

Temperature and pressure are essential for describing the air's thermal properties and mechanical behavior, but they tell only part of the story. The complete state of the air also depends on other factors like the volume of the room and the number of air particles.
04

Consider an example

For instance, let's consider two isolated rooms with the same volume and temperature. In both cases, the pressure is the same. However, if one room has more air particles than the other, it will have a higher mass and will hence behave differently under certain conditions (e.g., when heated). In this case, knowing only the temperature and the pressure is not enough to fully describe the state of the air in both rooms.
05

Explain your conclusion

In conclusion, the state of the air in an isolated room is not completely specified by the temperature and the pressure alone. While these quantities are essential, they must also be accompanied by information on other variables like volume and the number of air particles in order to fully describe the state of the air.

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