Chapter 10, Problem 10.83QP

(a)

Interpretation Introduction

Interpretation: The phase of water that exists under the given conditions is to be predicted.

Concept introduction: Triple point is a point present in the pressure- temperature graph. It is defined as the point at which all the three phases of a substance coexist in equilibrium with each other at a time.

Critical point is a point present in the pressure- temperature graph where two phases that is liquid and gas coexist in equilibrium. At this point gaseous and liquid states are indistinguishable from each other.

In the phase diagram different phases of a substance are representated graphically at different temperatures and pressures.

To determine: The phase of water that exists at $\text{2}\text{atm}$ of pressure and $\text{110}\text{°C}$.

Answer to Problem 10.83QP

Solution

The liquid phase of water exists at $\text{2}\text{atm}$ of pressure and $\text{110}\text{°C}$.

Explanation of Solution

Explanation

The phase diagram of water at $\text{2}\text{atm}$ of pressure and $\text{110}\text{°C}$ is given below.

Figure 1

In the above Figure, a point is obtained when perpendicular line is drawn from $\text{110}\text{°C}$ of temperature and $\text{2}\text{atm}$ of pressure on the axes of the pressure- temperature graph.

This point corresponds to the initial condition that is $\text{2}\text{atm}$ of pressure and $\text{110}\text{°C}$ of temperature and is denoted by A.

Point A is in the liquid phase in the above figure.

So, water is liquid at the $\text{2}\text{atm}$ of pressure and $\text{110}\text{°C}$.

(b)

Interpretation Introduction

To determine: The phase of water that exists at $\text{200}\text{atm}$ of pressure and $\text{380}\text{°C}$.

Answer to Problem 10.83QP

Solution

Water is in the gas phase at $\text{200}\text{atm}$ of pressure and $\text{380}\text{°C}$.

Explanation of Solution

Explanation

The phase diagram of water at $\text{200}\text{atm}$ of pressure and $\text{380}\text{°C}$ is given below.

Figure 2

In the above Figure, The critical point of water exist at $\text{374}\text{°C}$ of temperature and at $\text{218}\text{atm}$ of pressure.

The phase of water at $\text{200}\text{atm}$ of pressure and $\text{380}\text{°C}$ of temperature is shown by a point B in the above Figure. This point is in the gas phase.

So, water exists in the gas phase at $\text{200}\text{atm}$ of pressure and $\text{380}\text{°C}$ of temperature.

(c)

Interpretation Introduction

To determine: The phase of water that exists at $6.0\times {10}^{-3}\text{atm}$ of pressure and $\text{0}\text{°C}$.

Answer to Problem 10.83QP

Solution

Water is in solid phase at $6.0\times {10}^{-3}\text{atm}$ of pressure and $\text{0}\text{°C}$.

Explanation of Solution

Explanation

The phase diagram of water at $6.0\times {10}^{-3}\text{atm}$ of pressure and $\text{0}\text{°C}$ is given below.

Figure 3

In the above Figure, the triple point of water is at temperature of $\text{0}\text{.010}\text{°C}$ and pressure of $0.0060\text{atm}$. The points correspond to $6.0\times {10}^{-3}\text{atm}$ of pressure which is equal to $0.0060\text{atm}$ and $\text{0}\text{°C}$ of temperature is shown as point C in the above figure.

The temperature $\text{0}\text{°C}$ is just below the triple point.

So, in the above Figure, point C is in the solid phase.

Therefore, Water is in solid phase exists at $6.0\times {10}^{-3}\text{atm}$ of pressure and $\text{0}\text{°C}$.

Conclusion

1. a) The liquid phase of water exists at $\text{2}\text{atm}$ of pressure and $\text{110}\text{°C}$.
2. b) Water is in gas phase at $\text{200}\text{atm}$ of pressure and $\text{380}\text{°C}$.
3. c) Water is in solid phase at $6.0\times {10}^{-3}\text{atm}$ of pressure and $\text{0}\text{°C}$.