Final answer:
In this problem, we are given the initial conditions of a piston-cylinder device containing an ideal gas. We are asked to determine the gas constant, molar mass of the gas, constant-volume and constant-pressure specific heats of the gas. We are also given the compression work done during the cooling process. To solve this problem, we can use the ideal gas law equation, as well as equations for adiabatic compression and expansion.
Step-by-step explanation:
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
(a) Number of moles of gas in each compartment:
Since we are given the volume, temperature, and pressure, we can rearrange the ideal gas law equation to solve for the number of moles:
n = PV / RT
Using the given values for the initial condition of each compartment, we can calculate the number of moles of gas in each compartment.
(b) Final volume of both gases:
Since the compression of B is adiabatic, we can use the adiabatic equation:
P₁V₁^y = P₂V₂^y
Where P₁ and P₂ are the initial and final pressures, V₁ and V₂ are the initial and final volumes, and y is the specific heat ratio.
Using the given values for the initial and final pressures, we can solve for the final volume.
(c) Final temperatures:
Since the compression and expansion processes are adiabatic, we can use the adiabatic equation:
T₁V₁^(y-1) = T₂V₂^(y-1)
Where T₁ and T₂ are the initial and final temperatures, and V₁ and V₂ are the initial and final volumes.
Using the given values for the initial and final volumes, we can solve for the final temperatures.
(d) Compression work:
The compression work done during this process is given as 16.6 kJ.