7. When analyzing the Carnot cycle, we found that for a reversible, adiabatic expansion of an ideal gas the initial temperature and volume (T,, V.) were related to the final temperature and volume (T, V) by (derived by relating the change in internal energy to work). C,In T = -nRln (1) a) If 1 mole of ideal gas (C, = R) initially at 500 K doubles in volume during an adiabatic expansion, what is its final temperature? b) Draw a temperature/volume graph of a thermodynamic cycle with three different steps (in any order): Step 1: adiabatic expansion, Step 2: constant volume heating/cooling, Step 3: isothermal expansion/compression. c) Prove Equation 1 by computing the entropy change for the three steps of the ther- modynamic cycle.
7. When analyzing the Carnot cycle, we found that for a reversible, adiabatic expansion of an ideal gas the initial temperature and volume (T,, V.) were related to the final temperature and volume (T, V) by (derived by relating the change in internal energy to work). C,In T = -nRln (1) a) If 1 mole of ideal gas (C, = R) initially at 500 K doubles in volume during an adiabatic expansion, what is its final temperature? b) Draw a temperature/volume graph of a thermodynamic cycle with three different steps (in any order): Step 1: adiabatic expansion, Step 2: constant volume heating/cooling, Step 3: isothermal expansion/compression. c) Prove Equation 1 by computing the entropy change for the three steps of the ther- modynamic cycle.
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Transcribed Image Text:7. When analyzing the Carnot cycle, we found that for a reversible, adiabatic expansion of
an ideal gas the initial temperature and volume (T, V;) were related to the final temperature
and volume (T7, V/) by (derived by relating the change in internal energy to work).
C„In
-nRln-
(1)
a) If 1 mole of ideal gas (C, = R) initially at 500 K doubles in volume during an
adiabatic expansion, what is its final temperature?
b) Draw a temperature/volume graph of a thermodynamic cycle with three different
steps (in any order): Step 1: adiabatic expansion, Step 2: constant volume heating/cooling,
Step 3: isothermal expansion/compression.
c) Prove Equation 1 by computing the entropy change for the three steps of the ther-
modynamic cycle.
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