Question

Ideal gas with Cp=32

State 1 (P=1bar T=300 k) compressed isothermally volume becomes 1/2 (state 2),

State 3 gas is compressed adiabatic to P₃=4 bar,

State 4 ideal gas is expanded isothermally to unknown P₄.

Finally gas is compresses back to stage 1.

Fill the blanks in the table for both T and P in all states showing your work

	Pressure P (bar)	Temperature T (K)
State 1	1	300
State 2
State 3	4
State 4

Answer 1

Given:

For 1 mole of gas

Step 1

Isothermal Compression

Hence, temeperature remains constant.

from

hence,

For an ideal gas, PV = constant for an isothermal process.

Hence,

Step 2

Adiabatic Compression.

Increasing pressure to 4 bar without heat or mass transfer to the system.

Also, for an ideal gas

hence,

Now,

here we have used ideal gas equation for 1 moles of gas PV = RT , Hence, V = RT/P.

Since R is a constant we can tak eit to the side of constant.

Using the values of .

Now,

Step 3

Isothermal expansion

Since this process is isothermal,

Again, using the relation

We cannot determine the unknown P4 as we do not know to what volume the isothermal expansion has been done. As heat is added to maintain the temperature at a constant volume, as long as the heat is being added, the system will keep expanding and the value of PV is going to be constant throughout.

	Pressure (bar)	temeprature (K)
State 1	1	300
State 2	2	300
State 3	4	359
State 4	?	359