An air compressor is a device that pumps air particles into a tank. A particular air compressor adds air particles to its tank until the particle density of the inside air is 40 times that of the outside air. If the temperature inside the tank is the same as that outside, how does the pressure inside the tank compare to the pressure outside? Assume atmospheric pressure equal to 100,000 Pa.

To determine how the pressure inside the tank compares to the pressure outside, we need to consider the relationship between pressure and particle density in a gas.

According to the ideal gas law, the pressure of a gas is directly proportional to its particle density (or number of particles) and the temperature of the gas. It can be expressed as:

Pressure = (Particle Density) × (Temperature) × (Gas Constant)

In this case, we are assuming that the temperature inside and outside the tank is the same. Therefore, the ratio of pressure inside the tank to pressure outside can be expressed as:

(Pressure inside) / (Pressure outside) = (Particle Density inside) / (Particle Density outside)

Given that the particle density inside the tank is 40 times that of the outside air, we can substitute this information into the equation:

(Pressure inside) / (Pressure outside) = 40

Next, we need to determine the pressure outside the tank. The problem states that the atmospheric pressure is 100,000 Pa. Therefore, the pressure outside the tank is 100,000 Pa.

Now, we can solve for the pressure inside the tank:

(Pressure inside) / (100,000 Pa) = 40

Cross-multiplying, we find:

Pressure inside = 40 × 100,000 Pa = 4,000,000 Pa

Therefore, the pressure inside the tank is 4,000,000 Pa, which is 40 times greater than the pressure outside.

SHREK AINT DREK