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Characteristics of Matter

At a certain ...

Question

At a certain temperature and pressure, ice, water and steam are found to coexist at equilibrium. This pressure and temperature corresponds to:

A

the critical temperature

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B

the critical pressure

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C

the sublimation point

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D

the triple point

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E

two of the above

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Solution

The correct option is D the triple point
At triple point of a substance is the temperature and pressure at which all three states of that substance coexist.

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Q. Assertion :At room temperature water does not sublimate from ice to steam. Reason: The critical point of water is much above the room temperature.

The essential conditions for liquefaction of gases were discovered by Andrews in

1869

as a result of his study of pressure-volume-temperature relationship for

C O_{2}

. It was found that above a certain temperature, it was impossible to liquefy a gas whatever the pressure was applied. The temperature below which the gas can be liquefied by the application of pressure alone is called critical temperature

(T_{c})

. The pressure required to liquefy a gas at this temperature is called the critical pressure

(P_{c)}

. The volume occupied by one mole of the substance at the critical temperature and pressure is called critical volume. Critical constants are related with van der Waals' constant as follows:

V_{c} = 3 b, P_{c} = \frac{a}{27 b^{2}}, T_{c} = \frac{8 a}{27 R b}

.

The relationship between

P_{C}, V_{C}

T_{C}

The essential conditions for liquefaction of gases were discovered by Andrews in

1869

as a result of his study of pressure-volume-temperature relationship for

C O_{2}

. It was found that above a certain temperature, it was impossible to liquefy a gas whatever the pressure was applied. The temperature below which the gas can be liquefied by the application of pressure alone is called critical temperature

(T_{c})

. The pressure required to liquefy a gas at this temperature is called the critical pressure

(P_{c)}

. The volume occupied by one mole of the substance at the critical temperature and pressure is called critical volume. Critical constants are related with van der Waals' constant as follows:

V_{c} = 3 b, P_{c} = \frac{a}{27 b^{2}}, T_{c} = \frac{8 a}{27 R b}

.

Which of the following parameters is three times the van der Waals' constant

^{'} b^{'}

?

Q. For many substances, there exists a temperature

T_{t r}

. and a pressure ptr at which all the three phases of a substance (gaseous, liquid, and solid) are in equilibrium. These temperature and pressure are known as the triple point. For example,

T_{t r} = {0.0075}^{\circ} C

p_{t r} = 4.58 m m

Hg for water. The latent heat of vaporization of water at the triple point is

q = 2.48 \times 10^{3} k J / k g

, and the latent heat of fusion of ice is

λ = 0.34 \times 10^{3} k J / k g

.
Find the latent heat

v

of sublimation (i.e. a direct transition from the solid to the gaseous state) of water at the triple point.

Q. Assertion :The critical temperature of

C O_{2}

is 304 K, it cannot be liquefied above 304 K. Reason: At a certain temperature, volume

\propto \frac{1}{pressure}

.

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