(II) A typical scuba tank, when fully charged, contains 12 L of air at 204 atm. Assume an "empty

(II) A typical scuba tank, when fully charged, contains 12 L...

(II) A typical scuba tank, when fully charged, contains 12 $\mathrm{L}$ of air at 204 atm. Assume an "empty" tank contains air at 34 atm and is connected to an air compressor at sea level. The air compressor intakes air from the atmosphere compresses it to high pressure, and then inputs this high- pressure air into the scuba tank. If the (average) flow rate of air from the atmosphere into the intake port of the air compressor is 290 $\mathrm{L} / \mathrm{min}$ , how long will it take to fully charge the scuba tank? Assume the tank remains at the, same temperature as the surrounding air during the filling process.

(II) A typical scuba tank, when fully charged, contains 12 $\mathrm{L}$ of air at 204 atm. Assume an "empty" tank contains air at 34 atm and is connected to an air compressor at sea level. The air compressor intakes air from the atmosphere compresses it to high pressure, and then inputs this high-
pressure air into the scuba tank. If the (average) flow rate of air from the atmosphere into the intake port of the air compressor is 290 $\mathrm{L} / \mathrm{min}$ , how long will it take to fully charge the scuba tank? Assume the tank remains at the, same temperature as the surrounding air during the filling
process.

Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, and temperature of an ideal gas. This relationship allows us to determine the amount of gas or the change in volume when pressure and temperature are varied, assuming the gas behaves ideally. It is fundamental in solving problems involving gas compression or expansion under varying conditions.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant throughout. Under these conditions, the product of pressure and volume remains constant (P?V? = P?V?), a formulation known as Boyle's law. This principle allows calculation of volume changes solely based on pressure variations, which is essential when analyzing compressed gas scenarios at a constant temperature.

Flow Rate Conversion

Flow rate conversion involves translating a given volumetric flow rate at one set of conditions (such as atmospheric pressure) to the corresponding conditions after compression. This is crucial for determining the time required to fill a container by relating the continuous input of gas volume to the gas's behavior under different pressures.

Unit Conversion in Gas Dynamics

Unit conversion in gas dynamics includes converting between different units of pressure and volume, ensuring consistency when applying gas laws. For instance, converting measurements like liters at one pressure to equivalent volumes at another pressure enables accurate calculations of gas quantities and process durations.

Transcript

00:01 A typical scuba tank when fully charged contains 12 litres of air at 204 atmospheres of pressure.

00:09 Assume an empty tank contains air at 34 atmospheres and is connected to an air compressor at sea level.

00:16 And the air compressor intake air from the atmosphere, converts it to high pressure and then inputs this high pressure air into the scuba tank.

00:25 If the average flow rate of the air from the atmosphere into the intake port of the air compressor is $2004.

00:30 90 liters per minute, how long will it fully take to charge the scuba tank? assuming the tank remains at the same temperature as the surrounding air during the filling process.

00:40 Right, okay, so we're going to start on a new page because it's a very long worded question.

00:46 However, we need to break down the question into what it's actually asking us.

00:50 So we're going to start from the ideal gas loss.

00:52 So p, but for two different scenarios, so p1, v1 equals n, 1, r, gas constant t1.

01:02 So pressure times volume equals number of moles times gas constant times temperature.

01:08 Call that equation 1 and similarly equation 2 we have p2 v2 equals n2 r t2 and we're going to call that equation 2 and we're going to do equation 1 divided by equation 2 which gives us p1 over p2 v1 over that doesn't look neat.

01:29 So p to the dot v1 over v2 is equal to n1 over n2 dot n2 dot t 1 over t 2 and the information that we're given in the question is that the gas is at the same temperature so we can immediately cancel these out because it's going to be the same so the fraction is just one.

02:01 Similarly, because the gas is being filled, we're going from one system whereby we're filling the tank with the set, no gas is lost in the process.

02:15 So we're filling from the atmosphere at sea level into the compressor, into the scuba time.

02:22 So no gas has been lost in this system.

02:25 So similarly, the number of moles that are being put into the tank are the same as the number of moles being taken out of the atmosphere.

02:33 So n1 is equal to n2.

02:36 So n1 over n2 is equal to 1.

02:38 And similarly, we can delete this fraction or it is simplified to 1 in this context...

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