The Physics
Hypertextbook
Opus in profectus

# Engines

## Practice

### practice problem 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.

### practice problem 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)
A Four Step Cycle (Adiabatic & Isochoric)
1. Determine the…
1. real efficiency
2. ideal efficiency (Carnot efficiency)
… of a heat engine running this cycle.

#### solution

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) 300 880 3,520 1,200
path A→B B→C C→D D→A ABCDA
description adiabatic isochoric adiabatic isochoric closed cycle
ΔU (J) +2,890 +13,160 −11,550 −4,500 0
Q (J) 0 +13,160 0 −4,500 +8,660
W (J) +2,890 0 −11,550 0 −8,660
A Four Step Cycle (Adiabatic & Isochoric)
1. it
2. it

### practice problem 3

Write something different.