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This problem was solved by the use of a thermodynamic process as well as an ideal gas equation.
Find the area below the P– V curve to find the work done on gas from states 1 through 2. State 2 to state 3. State 3 to sate 4. And state 4 to state 1. Add all the work done, i.e. 1->2->3->4 to find the total amount of work that was done on the gas in one cycle.
The last part of the equation is ideal gas equation. Find temperature for state 3.
Here is the equation of state for ideal gas:
Here, V is volume and P is pressure. N is the number moles. R is universal gas constant. T is ideal gas temperature.
Calculate the work that gas does in a thermodynamic process by using:
Gas’s work depends on its initial and final states, as well as the path.
This problem was solved by the use of a thermodynamic process as well as an ideal gas equation.
Find the area below the P– V curve to find the work done on gas from states 1 through 2. State 2 to state 3. State 3 to sate 4. And state 4 to state 1. Add all the work done, i.e.
to find the total amount of work that was done on the gas in one cycle.
The last part of the equation is ideal gas equation. Find temperature for state 3.
Here is the equation of state for ideal gas:
Here, V is volume and P is pressure. N is the number moles. R is universal gas constant. T is ideal gas temperature.
Calculate the work that gas does in a thermodynamic process by using:
Gas’s work depends on its initial and final states, as well as the path.
(A)
Calculated as follows:
Substitute
for
and
for
.
is required to replace
in the equation.
(B)
Calculated as follows:
During the transition from state 2 to 3 the volume of the gas remains constant. Substitute 0 for DV.
The gas is therefore cooled from state 2 to 3 at a temperature of 0.
(C)
According to the following calculation, the work on the gas from states 3 and 4 was:
Substitute
for
and
for
.
is required to replace
in the equation.
(D)
According to the following calculation, the work on the gas from states 4 to 1 was:
During the transition from state 4 to 1., the volume of the gas remains constant. Substitute 0 for DV.
The gas cools down from state 4 to 1 at a temperature of 0.
(E)
One cycle of gas work is:
Substitute
for
,
for
, 0 for
and
.
(F)
The following formula calculates the temperature at which the gas is in its state 1:
Substitute [katex]3p_0[/katex] for
or [katex]V_0[/katex] for
.
The following formula calculates the temperature at which the gas is in 3 state:
Substitute [katex]p_0[/katex] for
, and [katex]4V_0[/katex] for
.
Rearrange equation
to get the value of nR.
Use
in equation
.
The gas expansion from state 1 into state 2 was
.