# Carnot Heat Engine and Well-Insulated Piston Cylinder Systems

Problem 1 can only be solved per unit mass- eg work per unit mass, volume per unit mass, since there is not enough info to calculate the system mass.

Instructions: Solve the following problems. Be sure to include a sketch indicating the system and its interactions with the surroundings and state all necessary assumptions. Identify all relationships and provide symbolically before inserting numbers. Identify state models utilized and sources of necessary property data. Submitted should be neat and easy to follow. Sloppy work will not be graded.

1) The working fluid contained in a well-insulated piston cylinder is expanded in a quasi-equilibrium process from 1000oF and 350 [psia] until the temperature is 150oF. Calculate the final pressure and volume and the work done by the system if
a. the working fluid is oxygen and specific heat is constant, and
b. the working fluid is steam

2) The heat addition process of a Carnot heat engine utilizing a piston-cylinder mechanism is executed by vaporizing saturated liquid R134a at 100 [kPa] to saturated vapor.
a. What must be true about the pressure during this process? Why?
b. Calculate the heat added during the process
i. Using the first law.
ii. Using the second law

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#### Solution Preview

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where is the adiabatic exponent, assumed as constant since the specific heats are constant. For oxygen (like for all diatomic gases and the air), k = 1.4

If we work in metric units, we will have:

By applying (1), one yields:

The specific volume will be determined from the equation of state of the oxygen, considered as an ideal gas:
( 2)
where R = the gas constant,  = the universal gas constant ( = 8.314 kJ/kmol.K) and
molecular mass of oxygen ( 32 kg/kmol)

The (specific) work done can be computed by applying the 1-st law of Thermodynamics:
( 3)

b) For steam, we have to check first what the state 1 is ...