Question

A standard oxygen tank is rated for 3000 PSI of pressure. Any more than that, and it risks exploding. If an oxygen tank has 2500 PSI of pressure in it at room temperature (294 K), how hot could it get before reaching 3000 PSI of pressure?

Answer 1

To determine how hot an oxygen tank could get before reaching 3000 PSI of pressure, we need to use the ideal gas law equation. We can assume that the pressure is directly proportional to the temperature, so the tank could get approximately 3,447,380 K hotter before reaching 3000 PSI.

Step-by-step explanation:

To determine how hot an oxygen tank could get before reaching 3000 PSI of pressure, we need to use the ideal gas law equation: PV = nRT. Rearranging the equation to solve for temperature (T), we have T = PV / (nR), where P is the pressure, V is the volume, n is the number of moles, and R is the ideal gas constant.

Since the volume and number of moles are constant, we can simplify the equation to T = P / R, where R is the pressure in units of Pa and T is the temperature in Kelvin.

Let's plug in the given values:

T = (3000 PSI - 2500 PSI) / R = 500 PSI / R

Now we need to convert PSI to Pa. 1 PSI is equal to approximately 6894.76 Pa. Therefore, we have T = 500 PSI * 6894.76 Pa / R = 3,447,380 Pa / R.

Since the pressure conversion factor is really small compared to R, we can ignore it and assume that the pressure is directly proportional to the temperature. Therefore, the tank could get approximately 3,447,380 K hotter before reaching 3000 PSI of pressure.