Question

A) Find w12, the work done on the gas as it expands from state 1 to state 2.
Express the work done in terms of Po and Vo

B) Find W23 , the work done on the gas as it cools from state 2 to state 3.
Express your answer in terms of Po and Vo.

C) Find W34, the work done on the gas as it is compressed from state 3 to state 4.
Express your answer in terms of Po and Vo.

D) Find W41, the work done on the gas as it is heated from state 4 to state 1.
Express your answer in terms of Po and Vo .

E)What is Wnet, the total work done on the gas during one cycle?
Express your answer in terms of Po and Vo .

F) When the gas is in state 1, its temperature is T1. Find the temperature T3 of the gas when it is in state 3. (Keep in mind that this is an ideal gas.)
Express T3 in terms of T1.


The diagram shows the pressure and volume of an ideal gas during one cycle of an engine. As the gas proceeds from state 1 to state 2, it is heated at constant pressure. It is then cooled at constant volume, until it reaches state 3. The gas is then cooled at constant pressure to state 4. Finally, the gas is heated at constant volume until it returns to state 1.

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Answer 1

Concepts and reason

The main concept used to solve this problem is work done for a thermodynamic process and ideal gas equation.

Find out the area under the P-V curve and find out the work done on the gas from state 1 to state 2, state 2 to state 3, state 3 to sate 4 and state 4 to state 1. Add all the values of work done i.e. from and find the total work done on the gas during one cycle.

For the last part, use ideal gas equation and find temperature for state 3.

Fundamentals

The equation of state for an ideal gas is given as follows:

Here, P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant and T is the temperature of ideal gas.

The work done by gas for o thermodynamic process is calculated as:

The amount of work done by gas depends on initial and final state and the path also.

(A)

The work done on the gas from state 1 to state 2 is calculated as:

Substitute for , for and for in the above equation.

(B)

The work done on the gas from state 2 to state 3 is calculated as:

The volume of the gas is constant during the process from state 2 to state 3. Hence, substitute 0 for dV.

Therefore, the work done on the gas as it cools from state 2 to state 3 is 0.

(C)

The work done on the gas from state 3 to state 4 is calculated as:

Substitute for , for and for in the above equation.

(D)

The work done on the gas from state 4 to state 1 is calculated as:

The volume of the gas is constant during the process from state 4 to state 1. Hence, substitute 0 for dV.

Therefore, the work done on the gas as it cools from state 4 to state 1 is 0.

(E)

The work done on the gas during one cycle is:

Substitute for, for, 0 for and.

(F)

The temperature when the gas is in state 1 is calculated as:

Substitute for and for in the above equation.

The temperature when the gas is in state 3 is calculated as:

Substitute for and for in the above equation.

Re-arrange equation for the value of nR.

Use in equation.

Ans: Part A

The work done on the gas as it expands from state 1 to state 2 is .