Tina has a sample of gaseous water at a temperature of 400 C
and a pressure of 4 atm.
If Tina increases the pressure to 200 atm, will the gaseous water
liquefy? Why or why not?

The gaseous water will not liquefy since its new temperature is far higher that its initial temperature.

Explanation:

To know if the gaseous water will liquefy or not, we must first obtain the new temperature of the water. This can be obtained as follow:

Step 1:

Data obtained from the question:

Initial temperature (T1) = 400°C

Initial pressure (P1) = 4 atm

Final pressure (P2) = 200 atm

Final temperature (T2) =?

Step 2:

Conversion of celsius temperature to Kelvin temperature.

Temperature (Kelvin) = temperature (celsius) + 273

Initial temperature (T1) = 400°C = 400°C + 273 = 673K

Step 3:

Determination of the final temperature of the water.

Using the equation P1/T1 = P2/T2, the final temperature can obtain as follow:

P1/T1 = P2/T2

4/673 = 200/T2

Cross multiply to express in linear form

4 x T2 = 673 x 200

Divide both side by 4

T2 = (673 x 200) /4

T2 = 33650K

The final temperature of sample of gaseous water is 33650K

Step 4:

Conversion of Kelvin temperature to celsius temperature.

Temperature (celsius) = temperature (Kelvin) - 273

Temperature (celsius) = 33650K - 273

Temperature (celsius) = 33377°C

Therefore, the sample of the gaseous water will not liquefy since its new temperature is far higher that its initial temperature.