Pressure-Volume Diagrams

Problems

practice

  1. One mole of an ideal, monatomic gas runs through a four step cycle. All processes are either isobaric or isochoric. The pressure and volume of the gas at the extreme points in the cycle are given in the first two data rows of the table below.
    1. Sketch the PV graph of this cycle.
    2. Determine the temperature at state A, B, C, and D.
    3. Calculate W, Q, and ΔU on the path A→B, B→C, C→D, D→A and for one complete cycle. (Include the algebraic sign with each value.)
    4. Does this cycle behave more like an engine or a refrigerator?
               
    state A B C D  
     P (Pa)   100,000   200,000   200,000   100,000   
     V (m3)  0.020   0.020   0.060   0.060   
     T (K)           
    path A→B B→C C→D D→A ABCDA
     description   isochoric   isobaric   isochoric   isobaric  closed  cycle
     ΔU (J)           
     Q (J)           
     W (J)           
     
  2. Write something else.
  3. Write something different.
  4. Write something completely different.

conceptual

  1. Which requires more work: compressing a gas slowly so that its temperature remains equal to that of the environment (isothermal compression) or compressing a gas quickly so the heat that "wants" to escape does not have time to escape (adiabatic compression)? Justify your answer.

numerical

  1. Estimate the power of a relaxed human heart given an average blood pressure of 13 kPa, a volume change of 80 ml per beat, and a pulse rate of 72 beats per minute.
  2. Estimate the power of a pair of human lungs from the graph below given a respiration rate of 20 breaths per minute.
     
    [magnify]
     

  3. [magnify]
    One mole of an ideal gas runs through the zilch cycle, which consists of the following four processes …
       
    A→B  isothermal expansion at 600 K with 2.30 kJ of work done by the gas
    B→C  isochoric pressure drop
    C→D  isothermal expansion resumes at 300 K
    D→A  adiabatic compression returns the gas to its original state with 3.74 kJ of work done on the gas
       
    The cycle is rigged so that no net work is done over a complete cycle. The zilch cycle has no practical use. It's just an interesting thought problem. Given this information, complete the following table.
             
    path description ΔU(kJ) Q(kJ) W(kJ)
    A→B isothermal     −2.30
    B→C isochoric      
    C→D isothermal      
    D→A adiabatic     +3.74
    ABCDA closed cycle     0
     
  4. 0.40 moles of an ideal, monatomic gas runs through a four step cycle. All processes are either adiabatic or isochoric. The pressure and volume of the gas at the extreme points in the cycle are given in the first two data rows of the table below.
    1. Sketch the PV graph of this cycle.
    2. Determine the temperature at state A, B, C, and D.
    3. Calculate W, Q, and ΔU on the path A→B, B→C, C→D, D→A and for one complete cycle. (Include the algebraic sign with each value.)
    4. Does this cycle behave more like an engine or a refrigerator?
               
    state A B C D  
     P (Pa)   100,000   1,462,000   5,850,000   400,000   
     V (m3)  0.010   0.002   0.002   0.010   
     T (K)   
    path A→B B→C C→D D→A ABCDA
     description   adiabatic   isochoric   adiabatic   isochoric  closed  cycle
     ΔU (J)           
     Q (J)           
     W (J)           
     

The Physics Hypertextbook

  • No condition is permanent.