Question

Assume all temperatures to be exact, and neglect significant figures for small changes in dimension. A scuba diver takes a tank of air on a deep dive. The tank's volume is 10 L and it is completely filled with air at an absolute pressure of 239 atm at the start of the dive. The air temperature at the surface is 94 °F and the diver ends up in deep water at 57 °F. Assuming thermal equilibrium and neglecting air loss, determine the absolute internal pressure of the air when it is cold.

Answer 1

Using the Combined Gas Law and converting temperatures to Kelvin, the absolute internal pressure of the air in the tank when it is cold (57 °F) is found to be approximately 222.528 atm.

Step-by-step explanation:

To determine the absolute internal pressure of the air in the scuba tank when it reaches a temperature of 57 °F, we can use the Combined Gas Law, which relates pressure (P), volume (V), and temperature (T) of a gas. The Combined Gas Law formula is P1 × V1 / T1 = P2 × V2 / T2, where the subscripts 1 and 2 refer to the initial and final conditions respectively.

First, we need to convert the temperatures from Fahrenheit to Kelvin. The initial temperature at the surface is 94 °F, which is approximately 307.039 K, and the final temperature at depth is 57 °F, which is approximately 286.483 K.

Since the volume of the tank remains constant, we can simplify the equation to P1 / T1 = P2 / T2.

With the absolute pressure initially at 239 atm, we can plug in our values: (239 atm) / (307.039 K) = P2 / (286.483 K).

Solving for P2 gives us an absolute pressure of approximately 222.528 atm when the air is cold.