The Thermodynamic Cycle

Heat engines and refrigerators operate on thermodynamic cycles where a gas is carried from an initial state through a number of intermediate states and ultimately returned to its initial state. During a thermodynamic cycle: Heat Engines convert a portion of the heat input to work Refrigerators convert input work to the transfer of heat from low temperature to high temperature Examples: Steam engine Internal gas combustion engine Diesel engine Examples: Refrigerator Heat Pump

4.5 moles of O 2 are carried through a thermodynamic cycle composed of four steps: The molar specific heats for oxygen are:

What is the gas temperature at point "i"?

What is the gas temperature at point "1"?

What is the gas temperature at point "2"?

What is the gas volume at point "3"?

Summary When an ideal gas is carried through a complete cycle returning it to its initial state the net change in thermal energy is zero.

What is the efficiency of this heat engine?

Why is the molar specific heat at constant pressure, C P, always greater than the molar specific heat at constant volume, C V ? Recall: The specific heat of a substance is the amount of heat required to change the temperature of 1kg of the substance by 1C°,(or 1K). The equation relating heat flow and change in temperature is: Q=mc  T, or Q=nC  T. From the second equation an expression for molar specific heat can be obtained:

Suppose we take two containers each holding 1 mole of the same gas. We will take the first contained gas through an isobaric expansion process where heat Q=1000J flows into the gas and the gas does 200J of work. We will take the second contained gas through an isochoric expansion process where heat Q=1000J flows into the gas and the gas does no work. For an ideal gas the thermal energy, U only depends on the temperature, T. Let’s say that for every 100J change in thermal energy there is a corresponding 1C° change in the temperature.