25 litre bottle of oxygen in a hospital. If the bottle is at 12 atmospheres, what volume of oxygen is available to the patient? If the oxygen is stored at 4 degrees C and used at 20 degrees, what difference does this make? (Assuming start volume and pressure are still 25 litres and 12 atmospheres).

Question

25 litre bottle of oxygen in a hospital. If the bottle is at 12 atmospheres, what volume of oxygen is available to the patient? If the oxygen is stored at 4 degrees C and used at 20 degrees, what difference does this make? (Assuming start volume and pressure are still 25 litres and 12 atmospheres).

Answer 1

I wonder what 12 atmospheres means? Is that absolute pressure,or guage pressure?

P1V1=P2V2
solve for V2.

FOr the second question..

P1V1/T1=P2V2/T2 temps in Kelvins. Solve for V2

Answer 2

Thanks. Also noted that V2 would only be 275 as once the pressure in the bottle reaches 1atm, the volume inside would be 25litres. So only 275litres are available.

Answer 3

To calculate the volume of oxygen available to the patient, we can use Boyle's law, which states that the volume of a gas is inversely proportional to its pressure, assuming constant temperature.

Let's first convert the pressure from atmospheres (atm) to Pascals (Pa). 1 atm is approximately equal to 101325 Pa.

12 atm * 101325 Pa/atm = 1215900 Pa

According to Boyle's law, we can set up the following equation:

P1 * V1 = P2 * V2

Where:
P1 = initial pressure (1215900 Pa)
V1 = initial volume (25 liters)
P2 = final pressure (unknown)
V2 = final volume (to be determined)

Rearranging the equation, we have:

V2 = (P1 * V1)/ P2

V2 = (1215900 * 25)/ P2

Now, since we have the initial volume (V1) and pressure (P1), and we need to find the final volume (V2) at an unknown pressure (P2), we can use this equation to solve for V2, which represents the volume of oxygen available to the patient.

Now, let's consider the change in temperature from 4 degrees Celsius to 20 degrees Celsius. The change in temperature affects the pressure by altering the volume of the gas. To account for this change, we can use the Combined Gas Law, which combines Boyle's law, Charles's law, and Gay-Lussac's law.

The Combined Gas Law equation is:

(P1 * V1)/ T1 = (P2 * V2)/ T2

Where:
T1 = initial temperature (in Kelvin) = 4 + 273.15 = 277.15 K
T2 = final temperature (in Kelvin) = 20 + 273.15 = 293.15 K

Let's substitute the known values into the equation:

(1215900 * 25)/ 277.15 = (P2 * V2)/ 293.15

Now, solve for P2 * V2:

(P2 * V2) = (1215900 * 25 * 293.15)/ 277.15

Next, we need to convert the final temperature back to degrees Celsius and calculate V2:

V2 = (1215900 * 25 * 293.15 * (20 + 273.15))/(277.15 * 293.15)

Simplifying the equation will provide the final volume of oxygen available to the patient.

Note: Make sure to double-check the units and take into account any rounding if necessary.