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We have seen that the Carnot cycle can be used to determine the maximum efficiency of...

We have seen that the Carnot cycle can be used to determine the maximum efficiency of a heat engine. The efficiency is defined as the sum of all of the work during the cycle divided by the amount of heat exchanged during the expansion process:

efficiency=?1 +?2 +?3 +?3 /?1

Theoretically, the efficiency of the engine can be determined with the hot and cold temperature of the cycle.

efficiency = ?h − ?c/ ?h

In this problem, we will calculate the efficiency of two engines that have the same ?h and ?c values, so that we can determine if simply using the temperatures to determine the efficiency is valid. Both engines employ 1.0 mol of an ideal gas as the working substance in the engine. The constant volume heat capacity of this gas is CV = 25 J/mol K.

Engine 1: (begins at a pressure of 10.0 atm and a temperature of 327°C)

Process 1: The gas expands isothermally to a pressure of 1.0 atm

Process 2: The gas continues its expansion adiabatically until it reaches a temperature of 27°C

Process 3: The gas is compressed isothermally to a pressure of 10.0 atm

Process 4: The gas is compressed adiabatically, until it reaches a temperature of 327°C.

a. Calculate the work and heat for each process. (label as ?1 and ?2 for the work and heat associated with Process 1, etc.)

b. Using the first equation for efficiency, determine the efficiency of this engine.

c. Using the second equation for efficiency, determine the efficiency of this engine.

Engine 2: (begins at a pressure of 100.0 atm and a temperature of 327°C)

Process 1: The gas expands isothermally to a pressure of 1.0 atm

Process 2: The gas continues its expansion adiabatically until it reaches a temperature of 27°C

Process 3: The gas is compressed isothermally to a pressure of 1.0 atm (don't know final pressure)

Process 4: The gas is compressed adiabatically, until it reaches a temperature of 327°C.

d. Calculate the work and heat for each process. (label as ?1 and ?1 for the work and heat associated with Process 1, etc.)

e. Using the first equation for efficiency, determine the efficiency of this engine.

f. Using the second equation for efficiency, determine the efficiency of this engine.

g. What do your results tell you?

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