Write the significance of relative pressure and relative volume in the analysis of gas power cycles.
Answers
Answer:
Thermodynamic properties of gases
Gas cycles would not be possible in their current form if gases did not possess a peculiar set of properties, which will shortly be described in this section. The description will start with ideal gases, for which the mathematical equations that allow modelling of their behaviour are simple and can be easily integrated and derived.
The behaviour of an ideal gas can be summarised as follows:
1.
the equation of state is pv = RT;
2.
from (1) it can be demonstrated that the internal energy is a function of temperature only, u = f(T);
3.
from (2) and the definition of the specific heat at constant volume cv = ∂u/∂T, it follows that cv = f(T) and du = cvdT for any infinitesimal process;
4.
from the definition of enthalpy h = u + pv, it follows that enthalpy is also a function of T only, h = f(T);
5.
from (4) and the definition of the specific heat at constant pressure cp = ∂h/∂T it follows that cp = f(T), and that dh = cpdT, and eventually that cp–cv = R;
6.
from all the above equations, if we also assume that the specific heats at constant volume and pressure are constant, instead of being a function of temperature, we may derive the following expressions for any process joining points 1 and 2:
[3.1]u2−u1=cv(T2−T1)
[3.2]h2−h1=cp(T2−T1)
[3.3]s2−s1=cvln
T2
T1
+Rln
v2
v1
=cpln
T2
T1
Rln
p2
p1
It is now possible to make some interesting considerations by examining the T-s diagram of an ideal gas (Fig. 3.1), where a set of constant pressure lines are shown. If we move along an isothermal process from any point of the p0 line to any other pressure, either higher or lower, Equation [3.3] reduces to: