3. A gas is confined in a 0.47-m-diameter cylinder by a piston, on which rests a weight. The mass of the piston and weight together is 150 kg. The atmospheric pressure is 101 kPa. (a)What is the pressure of the gas in kPa? (b) If the gas in the cylinder is heated, it expands, pushing the piston and weight upward. If the piston and weight are raised 0.83 m, what is the work done by the gas in kJ? What is the change in potential energy of the piston and weight?

(a) add the atmospheric pressure to (weight)/(area)

Use the combined weight, 150*g = 1470 N
P = 1470/[(pi/4)0.47^2] + 101,000 Pa
=

(b) work done = P* 0.83 m *(area)
P.E. change of piston and weight
= M g H
The difference is work done against the atmosphere.

109472.8933

15764.1401
1220.1

47.5 kg cylinder. does this wieght include the combined wieght of both cylinder and gas?

To find the pressure of the gas in kPa, we need to consider the forces acting on the piston and weight system.

(a) The total force exerted on the piston is the sum of the weight of the piston and the atmospheric pressure equal to the force exerted by the gas. The weight of the piston and weight system is given as 150 kg.

First, we need to calculate the force exerted by the weight of the piston and weight system:

Force = mass x acceleration due to gravity
Force = 150 kg x 9.8 m/s^2
Force = 1470 N

The net force on the piston is zero when the system is in equilibrium. Therefore, the force exerted by the gas is equal in magnitude and opposite in direction to the total force exerted on the piston. Thus,

Force exerted by the gas = atmospheric pressure + force due to weight of piston and weight system

Therefore, we need to rearrange and solve the equation to find the pressure of the gas:

Pressure of the gas = (Force exerted by the gas - Force due to weight) / Area

The area of the piston can be determined using the formula for the area of a circle:

Area = π x (radius)^2

Given that the diameter of the cylinder is 0.47 m, the radius is half of that:

Radius = 0.47 m / 2
Radius = 0.235 m

Now, we can substitute the values into the equation for pressure:

Pressure of the gas = (Force exerted by the gas - Force due to weight) / Area
Pressure of the gas = (1470 N - (150 kg x 9.8 m/s^2)) / (π x (0.235 m)^2)
Pressure of the gas = (1470 N - 1470 N) / (π x (0.235 m)^2)
Pressure of the gas ≈ 0 kPa

Therefore, the pressure of the gas in kPa is approximately 0 kPa.

(b) To find the work done by the gas, we can use the formula:

Work = Force x Distance

In this case, the force is equal to the pressure of the gas, and the distance is the height the piston and weight are raised.

Given that the piston and weight are raised by 0.83 m, and the pressure of the gas is zero (as calculated in part a), the work done by the gas is:

Work = 0 x 0.83 m
Work = 0 J

Therefore, the work done by the gas in kJ is 0 kJ.

The change in potential energy of the piston and weight is given by the formula:

Change in potential energy = Force x Height

In this case, the force is equal to the weight of the piston and weight system, and the height is the distance the piston and weight are raised.

Given that the weight of the piston and weight system is 150 kg, and the piston and weight are raised by 0.83 m, the change in potential energy is:

Change in potential energy = (150 kg x 9.8 m/s^2) x 0.83 m
Change in potential energy = 1227 J

Therefore, the change in potential energy of the piston and weight is 1227 J.