CONSTANTS:   1 cal = 4.186 J           1 atm = 1.01 x 10⁵ N/m²

1]   An ideal gas has a volume of 22.4 x 10^-3 m³ at zero degrees Celsius and one atmosphere
pressure.  The gas absorbs 315 cal of heat from the surroundings and expands isobarically to
32.4 x 10^-3 m³ .  What is the change in the internal energy of the gas?

Answer:  DU = 310 J
 

2]  A heat engine absorbs 1500 J of energy each cycle and exhausts 1000 J of energy each cycle.
Determine the maximum efficiency and work output per cycle of the engine.

Answer:   33% ,  500 J
 

3] An ideal heat engine is designed to produce 5000 J of work when it uses a hot reservoir
providing 12,500 J of heat energy. If the engine will typically have an exhaust temperature of
25 ^oC, what must the temperature of the hot reservoir be in degrees Celsius?

Answer: 224 degrees Celsius
 

4] A cylinder with a movable piston contains 9.0 grams of steam with the following properties:
pressure is 5.5 atmospheres, volume is 3.0 liters, temperature is 130 ^oC . Under constant
pressure, heat is added to the steam such that the piston moves up (volume increases) until the
steam temperature is 250 ^oC . What is the change in the internal energy of the steam for this
process?

Answer: +1700 J
 

5] A heat engine is designed to produce 3000 J of work when it uses a hot reservoir of
temperature 200 ^oC and has an exhaust temperature of 25 ^oC. Determine the maximum
efficiency of the engine and the heat lost to the surroundings each cycle.

Answer: e = 37% , Q = 5100 J
 

6] 100 grams of water is in a closed container of volume 500 cm³ . At a constant pressure of
2.50 atmospheres and a constant temperature of 100 ^oC, the water is turned into steam that
fills the container. What is the change in the internal energy of the water molecules for this
process?

Answer: 2.26 x 10(5) Joules
 

M ULTIPLE CHOICE

1)   An ideal gas is quickly compressed in an insulated environment.  During this process, the gas exchanges no energy
       (or heat) with its surroundings.  The process is thus an  ___________  process.

       a.  isothermal
       b.  isometric
       c.  isobaric
       d.  adiabatic

2)  An ideal gas is compressed to one-half its original volume during an isothermal process.  The final pressure of the gas

       a. increases to twice its original value
       b. increases to less than twice its original value
       c. increases to more than twice its original value
       d. does not change
       e.  decreases to one-half its original value

3)  When water freezes, the entropy of the water
   
       a.  increases
       b.  decreases
       c.  does not change
       d.  could either increase or decrease depending on the pressure

4)  The 2nd law of thermodynamics leads us to conclude that
   
       a.  the total energy of the universe is constant
       b.  disorder in the universe is increasing with the passage of time
       c.  it is theoretically possible to convert energy into work with 100% efficiency
       d.  the average temperature of the universe is increasing with the passage of time

5)  The Carnot cycle is the most efficient heat engine cycle.  If the efficiency of a Carnot engine were to be
      %100, the exhaust reservoir would have to be

       a.  infinitely hot
       b.  at a temperature of 0 degrees Celsius
       c.  at a temperature of 100 degrees Celsius
       d.  at absolute zero
       e.  at any tempertures since a Carnot engine always has 100% efficiency

Answers

1.   d
2.   a
3.   b
4.   b
5.   d