In the following graph, a reversible Carnot cycle for an ideal gas is shown in «pressure-temperature — Analytical Chemistry Chemistry Question
Carnot cycle
In the following graph, a reversible Carnot cycle for an ideal gas is shown in «pressure-temperature» coordinates. A cycle consists of two isotherms and two adiabates.
Using this graph, calculate the following magnitudes or show that it is impossible:
The useful work of the cycle.
Model Answer
This is impossible because we do not know the number of moles of a gas.
The efficiency η of the cycle.
Model Answer
η = (T2 - T1) / T2 = (390 - 298) / 390 = 0.24.
The isochoric molar heat capacity of a gas.
Model Answer
Since in a reversible adiabatic process for an ideal gas pV^(1+R/CV) = const, then T*p^(-R/CV) = const. Thus, we can find CV from the initial and final temperatures and pressures of the adiabate. CV = 3 R.
The number of atoms in the molecule of a gas.
Hint: In reversible adiabatic process for an ideal gas, pV^(1+R/CV) = const where CV is the isochoric molar heat capacity.
Model Answer
It can be any number from 3 and above (the molecule should be non-linear).