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 phy131studiof15:lectures:finalp1sol [2015/12/02 09:34]mdawber [Question 5] phy131studiof15:lectures:finalp1sol [2015/12/02 09:36] (current)mdawber [Question 6] Both sides previous revision Previous revision 2015/12/02 09:36 mdawber [Question 6] 2015/12/02 09:36 mdawber [Question 6] 2015/12/02 09:36 mdawber [Question 6] 2015/12/02 09:34 mdawber [Question 5] 2015/12/02 09:30 mdawber [Question 4] 2015/12/02 09:29 mdawber [Question 3] 2015/12/02 09:27 mdawber [Question 2] 2015/12/02 09:26 mdawber [Question 1] 2015/12/02 09:26 mdawber [Question 2] 2015/12/02 09:23 mdawber [Question 1] 2015/12/02 08:50 mdawber [Question 5] 2015/11/30 14:47 mdawber created Next revision Previous revision 2015/12/02 09:36 mdawber [Question 6] 2015/12/02 09:36 mdawber [Question 6] 2015/12/02 09:36 mdawber [Question 6] 2015/12/02 09:34 mdawber [Question 5] 2015/12/02 09:30 mdawber [Question 4] 2015/12/02 09:29 mdawber [Question 3] 2015/12/02 09:27 mdawber [Question 2] 2015/12/02 09:26 mdawber [Question 1] 2015/12/02 09:26 mdawber [Question 2] 2015/12/02 09:23 mdawber [Question 1] 2015/12/02 08:50 mdawber [Question 5] 2015/11/30 14:47 mdawber created Line 199: Line 199: ===== Question 6 ===== ===== Question 6 ===== - A. $e=\frac{W}{Q_{H}}$ + {{phy141f12finalq8fig.png}} + + The diagram shows the P-V diagram for a 40% efficient ideal Carnot engine. Assume the gas used in this Carnot engine is an ideal diatomic gas. + + A. (5 points) For every Joule of work obtained from the engine, how much heat needs to be added to engine? + + $e=\frac{W}{Q_{H}}$ $Q_{H}=\frac{1}{0.4}=2.5\mathrm{J}$ $Q_{H}=\frac{1}{0.4}=2.5\mathrm{J}$ - B.$Q_{H}=W+Q_{L}$ + B. (b) (5 points) For every Joule of work obtained from the engine how much heat is lost to the environment?​ + + $Q_{H}=W+Q_{L}$ $Q_{L}=1.5\mathrm{J}$ $Q_{L}=1.5\mathrm{J}$ - C. $P_{B}V_{B}=nRT_{H}$ + C. (5 points) At points B and D the gas in the system has the same volume, but different temperatures. If the gas at point D is at twice atmospheric pressure, what is the pressure of the gas at point B? + + $P_{B}V_{B}=nRT_{H}$ $P_{D}V_{D}=nRT_{L}$ $P_{D}V_{D}=nRT_{L}$ Line 221: Line 231: $P_{B}=3.33P_{atm}$ $P_{B}=3.33P_{atm}$ - D. The expansion from B to C is adiabatic so $P_{B}V_{B}^{\gamma}=P_{C}V_{C}^{\gamma}$ + D. (5 points) If the volume of the gas at point B is 1L what is the volume of the gas at point C? + + The expansion from B to C is adiabatic so $P_{B}V_{B}^{\gamma}=P_{C}V_{C}^{\gamma}$ For a diatomic gas $\gamma=\frac{7}{5}$ For a diatomic gas $\gamma=\frac{7}{5}$ Line 237: Line 249: $V_{C}=3.6\mathrm{L}$ $V_{C}=3.6\mathrm{L}$ - E. $\Delta S=0\mathrm{\frac{J}{K}}$ + E. (5 points) How much does the net entropy of the engine and the environment change for every Joule of work done by this Carnot engine? + + + $\Delta S=0\mathrm{\frac{J}{K}}$