A piston-cylinder device contains 100 g of ethylene gas initially at 27oC, 115 kPa. Ethylene is heated and the piston starts to rise until the volume reaches 90 L and merely touches a linear spring that has a spring constant of 60 kN/m. More heat is added until the piston rises 12 cm more. Assume the atmospheric pressure to be 102 kPa.

(a) If the piston has a diameter of 18 cm, how much does this piston weigh?
(b) What is the final pressure?
(c) What is the final temperature?
(d) Determine the internal energy and enthalpy change during the process.
(e) Show the process on a P-ν diagram.
(f) Determine the work done during this process and its direction.

To answer these questions, we need to apply the laws of thermodynamics and use the given information. Let's break down each question and explain the steps to find the answers.

(a) To find the weight of the piston, we need to determine its mass first. The mass can be calculated using the volume of the piston and the gas density. The density of the gas can be determined using the ideal gas law, which states:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.

First, we need to find the number of moles of ethylene gas. We can use the ideal gas law to solve for n:

n = PV / RT

We have the values: P = 115 kPa, V = 90 L (converted to m^3), T = 27°C (converted to Kelvin), and R = 8.314 J/mol·K.

Substituting the values into the equation, we can find the number of moles (n) of ethylene gas.

Once we have the number of moles, we can calculate the mass using the molar mass of ethylene (28.05 g/mol). Multiply the number of moles by the molar mass to get the mass in grams.

Finally, to find the weight of the piston, we need to multiply the mass by the acceleration due to gravity (approximately 9.8 m/s^2).

(b) The final pressure can be determined using the ideal gas law again. At the final state, the volume (90 L + 0.12 m^3) and temperature are given, and we can solve for the final pressure.

(c) The final temperature can be calculated using the ideal gas law once again. Since the final pressure and volume are known, we can rearrange the equation to solve for the final temperature.

(d) To determine the internal energy change, we use the first law of thermodynamics, which states that the change in internal energy (ΔU) is equal to the heat added (Q) minus the work done (W).

Internal Energy Change (ΔU) = Q - W

We can calculate the work done using the formula for the work done by a spring:

W = (1/2)kx^2

where k is the spring constant and x is the displacement of the spring.

To find the enthalpy change, we can use the equation:

Enthalpy Change (ΔH) = ΔU + PΔV

Where P is the pressure and ΔV is the change in volume.

(e) To show the process on a P-ν (pressure-volume) diagram, we need to plot points using the initial and final pressure and volume values. Connecting these points will give us a representation of the process on the diagram.

(f) The work done during the process can be calculated by integrating the pressure-volume curve on the P-ν diagram. Since the process is not given in detail in the question, we assume it to be an ideal gas process. The direction of work can be determined based on the change in volume and pressure.

By following these steps, you should be able to find the answers to all the questions regarding the given piston-cylinder system and the properties of the gas inside it.