Understanding Pressure Changes in Scuba Tanks: A Practical Guide

What is the pressure inside a scuba tank heated from 27°C to 42°C, starting at 2043 PSIG?

• A. 2043 PSIG
• B. 2146 PSIG
• C. 2200 PSIG
• D. 2300 PSIG

Answer: (B)

To determine the pressure change in a scuba tank when the temperature increases, we can apply Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its absolute temperature when the volume is held constant. In this scenario, you start with a pressure of 2043 PSIG at an initial temperature of 27°C. When converted to Kelvin, 27°C becomes 300.15 K. The final temperature of 42°C corresponds to 315.15 K in Kelvin. Using the relationship between pressure and temperature: P1/T1 = P2/T2 By substituting the known values into the equation: 2043 PSIG / 300.15 K = P2 / 315.15 K By rearranging the equation, you can solve for P2, which represents the pressure at 42°C: P2 = (2043 PSIG * 315.15 K) / 300.15 K After performing the calculations, it results in approximately 2146 PSIG. This value is consistent with the increase in pressure due to the temperature increase, confirming that the correct answer is indeed 2146 PSIG, as expected from Gay-Lussac's Law.

When it comes to scuba diving, understanding the relationship between temperature and pressure is crucial—especially if you're prepping for your Certified Hyperbaric Technologist exam. Picture this: you’ve just filled your scuba tank, the gauge reads 2043 PSIG, and you're ready for your dive. But what happens if the temperature rises from 27°C to 42°C? Let’s break down the steps to determine the new pressure inside that tank.

The Law Behind the Numbers

You might be familiar with Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its absolute temperature when the volume remains constant. What does that mean for you? Pretty much that as the temp in your scuba tank climbs, so does the pressure.

To get started, we’ll convert our temperatures to Kelvin. That’s where the magic happens! The initial temperature ( T_1 ) is 27°C, which becomes ( 300.15,K ) when we add 273.15. After a chill swim, it rises to 42°C, becoming ( 315.15,K ).

Plugging Into the Formula

Now, let’s take it step-by-step with the pressure equation:

[ \frac{P_1}{T_1} = \frac{P_2}{T_2} ]

In this equation:

• ( P_1 ) is the initial pressure—2043 PSIG in our case.

• ( T_1 ) is the initial absolute temperature—300.15 K.

• ( P_2 ) is what we’re solving for (the final pressure).

• ( T_2 ) is the final temperature of 315.15 K.

Rearranging that gives us:

[ P_2 = P_1 \times \frac{T_2}{T_1} ]

Substituting in the values, we get:

[ P_2 = 2043 \times \frac{315.15}{300.15} ]

So, what’s the outcome of that calculation? Drumroll, please... we arrive at approximately 2146 PSIG! This means your tank has gained pressure thanks to that temperature increase.

Why This Matters

Understanding this concept is more than just a number game; it’s about safety. Higher pressure can lead to complications if tanks are not managed properly. For a scuba diver or a hyperbaric technician, having a solid grasp of how these factors interact can inform important decisions—like when to check equipment or gauge whether a particular dive is safe.

Make It a Part of Your Study Routine

As you prepare for your exam, don’t underestimate the power of mastering such calculations. Try practicing with different temperatures and pressures, or even quiz your fellow students. Knowing how to apply principles like Gay-Lussac’s Law can not only help on the exam but can be a lifesaver in real-world scenarios.

By keeping this pressure-temperature relationship woven into your study routine, you're not just cramming; you're truly understanding the physics that will guide you in your future role as a Certified Hyperbaric Technologist. Dive into your studies with confidence, knowing that each piece of knowledge is another step toward success (and safety) in diving. Keep swimming toward your goals!