A gas is confined within a chamber with a cylindrical shape that has a moveable piston. The mass of the piston is 10.7 kg, and its radius is 0.03 m. If the system is in equilibrium, what is the pressure exerted on the piston by the gas? 1.61 x 105 Pa 3.71 x 104 Pa 1.01 x105Pa None of the above.
Question
A gas is confined within a chamber with a cylindrical shape that has a moveable piston. The mass of the piston is 10.7 kg, and its radius is 0.03 m. If the system is in equilibrium, what is the pressure exerted on the piston by the gas? 1.61 x 105 Pa 3.71 x 104 Pa 1.01 x105Pa None of the above.
Solution
To solve this problem, we need to use the formula for pressure, which is force divided by area.
Step 1: Calculate the force exerted by the piston. The force is the weight of the piston, which is its mass times the acceleration due to gravity.
Force = mass * gravity Force = 10.7 kg * 9.8 m/s^2 = 104.86 N
Step 2: Calculate the area of the piston. The piston is cylindrical in shape, so the area is the area of the circle at the top of the cylinder, which is pi times the radius squared.
Area = pi * radius^2 Area = 3.14 * (0.03 m)^2 = 0.00283 m^2
Step 3: Calculate the pressure. The pressure is the force divided by the area.
Pressure = Force / Area Pressure = 104.86 N / 0.00283 m^2 = 37094.7 Pa
So, the pressure exerted on the piston by the gas is approximately 3.71 x 10^4 Pa. Therefore, the correct answer is 3.71 x 10^4 Pa.
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