Engines

Problems

practice

  1. Needs to be fixed
    The human body is exceptionally efficient at extracting energy from food. Feces retain only about 5% of the chemical energy originally present in the food consumed. Most of this energy is going into basic maintainance or metabolic work. Efficiencies are lower when we look at the energy consumed that goes into mechanical work. Cycling is one of the most efficient activities that humans can engage in. For a trained cyclist, efficiencies approach 20% with mechanical work being generated at a rate of 370 W compared to a metabolic work of 1850 W. Cars are notoriously wasteful in comparison. Gasoline has an energy content of 477 MJ/kg and a density of 680 kg/m3. If a car can travel 8500 km per m3 of gasoline (8.5 km per liter or 15 mpg) the car will use 40 times more energy over the same distance.
  2. 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.)
               
    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)           
     
    1. Determine the …
      1. real efficiency
      2. ideal efficiency (Carnot efficiency)
      … of a heat engine running this cycle.
  3. Write something different.
  4. Write something completely different.

conceptual

  1. If your goal is to improve the theoretical efficiency of an engine, is it better to increase the temperature of the hot reservoir by a certain amount or decrease the temperature of the cold reservoir by the same amount? Justify your answer with calculations.

numerical

  1. A series of 4 connected questions about a human heart.
    1. A healthy adult heart pumps 80 mL of blood per contraction and contracts once each second. Blood pressure within the circulatory system varies from a maximum (systole) of 16 kPa (120 torr) to a minimum (diastole) of 10.7 kPa (80 torr). Determine the average power generated by a human heart.
    2. The heart actively works during one-third of each cycle and rests for the remaining two-thirds of the cycle. Determine the power generated by a human heart during the pumping phase.
    3. The mechanical efficiency of the heart is about 9% (only 9% of the energy it consumes goes to actual work). Determine the average power consumed by a human heart.
    4. During strenuous exercise, the heart pumps 5 times more blood per minute and blood pressure increases by 50%. Determine the average power consumed by an exercising human heart.
  2. Wärtsilä RTA96C (14 cylinder model)
    specification value
    displacement 25.48 cubic meters
    power 80.08 megawatts
    torque 7.604 meganewton meters
    rotational speed 102 rotations per minute
    fuel consumption 13,690 liters per hour
    fuel energy density 42.70 megajoules per liter
    peak pressure 14.5 megapascals
    The largest piston engines in the world are used to propel container ships. Some data for one of these large engines is given in the table to the right.
    1. Calculate the following quantities in gigajoules per hour …
      1. the heat produced by burning fuel
      2. the useful work done by the engine
      3. the heat exhausted to the environment
    2. What is the efficiency of this engine?

The Physics Hypertextbook

  • No condition is permanent.