00:01
In our question, we are given a three -step heat engine cycle that consists of an adiabatic expansion, isochoric compression and an isochoric process.
00:07
Now, the working substance consists of n moles of an ideal gas with a molar heat capacity at constant volume, cv, and a molar heat capacity at constant pressure, c of p.
00:19
Now, the cycle operates between pressures p1 and p2 and volumes v2 are shown in a figure.
00:24
We need to label the points on the graph with a, b or c and connect the points with properly shaped lines, representing each process.
00:33
Now the adiabatic line is a, b.
00:35
Here, the heat remains constant.
00:44
Therefore, del q is 0.
00:47
In the isobaric compression, that is a process for b, c, the pressure is constant.
00:56
Therefore, del p, that is pressure change is zero.
00:59
And in isochoric process, that is from c, a, the volume being constant, therefore the change in volume is 0.
01:10
Therefore the adiabatic expansion that is ab is a positive change given by v2 minus v1.
01:19
Isobar a compression bc is given by a negative change that is v1 v1 minus v2 and the isochoric process ca is given as a positive change with p2 minus p1 v1.
01:39
For our next case we have to calculate the heat, the work and the change in the internal energy.
01:52
Del u for each process in the cycle and express r answers in terms of pressure, volume, specific heat at constant volume and specific heat at constant pressure.
02:05
Now using thermodynamics first law, we know that heat exchange will be equivalent to the change in internal energy plus the work done, which we can write as, let this be equation 1, del d, be equal to plus p del v.
02:38
First consider case of the adiabatic process.
02:42
Now from equation 1 we get change in workdown equivalent to negative change in internal energy.
02:49
Let this be equation 2.
02:51
Now for an ideal gas we have the relation...