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13 Dec 2019

cyclic process

Consider an ideal gas with molar constant volume heat capacity, cV,m = 1.50 R. The gas undergoes the reversible four step cyclic process shown to the left: 1. During step 1, the gas expands isothermally from V1 to V2. 2. During step 2, the gas expands adiabatically from V2 to V3. 3. During step 3, the gas is compressed isothermally from V3 to V4. 4. During step 4, the gas is compressed adiabatically from V4 to V1. Given T1 = 350.0 K, P1 = 1.00 × 105 Pa, V1 = 5.82 × 10-2 m3 , V2 = 10.0 × 10-2 m3 , T3 = 175.0 K,

Perform the following calculations:

a. Determine the pressure, volume, and temperature of the gas at equilibrium points 1, 2, 3, and 4.

b. Calculate the work done on the gas during each step.

c. Calculate the transfer of energy into the gas as heat during each step.

d. Calculate the change in energy of the gas during each step.

e. Calculate q, w, and ΔU for the entire cyclic process.

f. Determine the enthalpy of the gas at equilibrium points 1, 2, 3, and 4.

g. Calculate the change in enthalpy of the gas during each step.

h. Calculate ΔH for the entire cyclic process.

i. Calculate the change in entropy of the gas during each step.

j. Calculate the change in entropy for the entire cyclic process

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Related questions

For the Carnot cycle assuming an ideal gas and reversible processes, determine the change in entropy, dSsys, of the system (not the surroundings) for each of these four steps.

Step 1: isothermal expansion from (V1,P1, T1) to (V2, P2, T1).

Step 2: adiabatic expansion from (V2, P2, T1) to (V3, P3, T2).

Step 3: isothermal compression from (V3, P3, T2) to (V4, P4, T2).

Step 4: adiabatic compression from (V4, P4, T2) to (V1,P1, T1)

THERMODYNAMICS

There is an engine, that has a 3 step process using 2.50 mole of an ideal gas law.

Step 1 the gas starts at point A where it has a volume of 1.00 L and a temperature of 300 K. The gas is then heated at constant volume until it reaches point B. At point B, the temp is 400 K.

Step 2: From point B, the gas is allowed to expand reversibly and isothermally until it reaches point C, where it has a volume of 1.33 L. The pressure at point C is the same is the pressure at point A.

For Step 3, from point C,the gas is then compressed at constant pressure conditions back to the original starting point A(1.00 L and 300 K).

Calculate the q,w, and delta U for each step in the cycle?

1. Equation shows the relation between T and V when an ideal gas is adiabatically and reversibly expanded or compressed from T1V1 to T2V2,

a) Prepare a table in an Excel spreadsheet showing the values of V, T, and p (i.e., three columns) when 200 g. CH4(g) is reversibly and adiabatically expanded starting at T1 = 350K, V1 = 0.010 m3 to a final volume of 200 L. Assume ideal gas behaviour. Needed heat capacity data can be found in the Lecture Notes Appendix.

In the first column, use values of V starting from V1 = 0.010 m3 to 200 L (0.200 m3) in steps of 0.010 m3 . In column 2 calculate each new T (eq. 2.42) and in column 3 the corresponding new pressure. Remember eq. 2.29.

b) Next prepare two separate graphs, one of T (y-axis) vs. V (L or m3, your choice) and one of p (y-axis) against V using the values from the columns in a). Present your table and graphs on the same page. Make sure your graphs include a title for each, axis legends (x-values V (m3), y-values T (K) or p (Pa).

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