Question

An engine that operates by means of an ideal diatomic ideal gas in a piston with 2.70 moles of gas. The gas starts at point A with 3x103 Pa of pressure and 2.5x10-2 m3. To get from B from A, it is expanded by an isobaric process to double the initial volume. From B to C it expands adiabatically until it reaches three times the volume in A. From C to D the pressure decreases without changing the volume and from D to A it is an isothermal compression. a) Draw the PV diagram of the process and determine the pressure and volume at each vertex. Calculate: b) full cycle work. C) The heat transferred in each process. D) The real efficiency and efficiency of carnot. D) The change of entropy in each process.

Forgive me, I'm a little bit vague on the detail.

Answer 1

a) the process can be represented using the PV diagram as shown below.

The curve BC is more steeper than AD

Now, the values of pressure and volume.

At A, the pressure and volume is given in the question.

A = (V,P) = (2.5*10^-2,3*10³)

At B, the volume is doubled, but the pressure remains the same

B = (V,P) = (5*10^-2,3*10³)

At C, the volume is 3 times the volume at A, but the pressure is now related by the equation

For a diatomic ideal gas,

So,

Here, V₂ = 3/2V₁

So,

So,

C = (V,P) = (7.5*10^-2,1.7*10³)

At D, the pressure is same, but the volume is determined by the isothermal equation from A to D

So,

D = (V,P) = (4.412*10^-2,1.7*10³)

b) The work done for each process is the area under the curve

So, total work done is

c) The heat transferred in an isobaric process is related to the work done by the relation (only for diatomic ideal gas)

So,

For adiabatic process, Q = 0

For isothermal process, heat transferred is equal to the work done

So, total heat transferred =

d) Efficiency of an engine is given as

The carnot efficiency is given by the quantity of maximum volume expansion

Where the points are the extremum of pressure and volume.(A and C)

e) For a non-ideal engine,the difference between the efficiencies is a result of change in internal energy

The difference in heat transferred is

The initial temperature of the system is

So,