Review Exercise 3-1 Answers

Part 1

Multiple-Choice: Circle the correct answer

 

1.  A container of an ideal gas at 1 atm is compressed to one-third its volume, with the

     temperature held constant.  What is its final pressure?

 

     A) 1/3 atm

 

     B) 1 atm

 

     C) 3 atm      Answer      PV = nRT         P = nRT/(V/3)  = 3nRT/V    if T is held constant, then P must increase by a factor of 3 to 3 atm

 

     D) 9 atm

 

2.  If the pressure acting on an ideal gas at constant temperature is tripled, its volume is

 

     A) reduced to one-third.       Answer    PV = nRT      V = nRT/(3P)     means that the volume is reduced by 1/3

 

     B) increased by a factor of three.

 

     C) increased by a factor of two.

 

     D) reduced to one-half.

 

3.  According to the ideal gas Law, PV = constant for a given temperature.  As a result, an

    increase in volume corresponds to a decrease in pressure.  This happens because the

    molecules

 

     A) collide with each other more frequently.

 

     B) move slower on the average.

 

     C) strike the container wall less often.     Answer 

 

     D) transfer less energy to the walls of the container each time they strike it.

 

4.  The number of molecules in one mole of a substance

 

     A) depends on the  molecular weight of the substance.

 

     B) depends on the atomic weight of the substance.

 

     C) depends on the density of the substance.

 

     D) is the same for all substances.     Answer       from the definition

 

5.  Both the pressure and volume of a given sample of an ideal gas double. This means that its

     temperature in Kelvin must

 

     A) double.

 

     B) quadruple.       Answer    PV = nRT      T = PV/nR       if the numerator on the right is quadrupled (2x2) then T must be quadrupled

 

     C) reduce to one-fourth its original value.

 

     D) remain unchanged.

 

6.  Consider two equal volumes of gas at a given temperature and pressure.  One gas, oxygen,

     has a molecular mass of 32.  The other gas, nitrogen, has a molecular mass of 28.  What is

     the ratio of the number of oxygen molecules to the number of nitrogen molecules?

 

     A) 32:28

 

     B) 28:32

 

     C) 1:1      Answer  By Avogadro's hypothesis they contain the same number of molecules.  The ratio is therefore 1 to 1

 

     D) none of the above

 

7.  The average molecular kinetic energy of a gas can be determined by knowing only

 

     A) the number of molecules in the gas.

 

     B) the volume of the gas.

 

     C) the pressure of the gas.

 

     D) the temperature of the gas.      Answer   Temperature (in K) of a gas is defined as the average kinetic energy of the molecules

 

8.  The amount of heat necessary to raise the temperature of 1 gram of water by 1°C is referred

     to as the  

 

     A) calorie.        Answer  definition

 

     B) kilocalorie.

 

     C) British thermal unit.

 

     D) joule.

 

9.  The measure of the average kinetic energy of individual molecules is referred to as  

 

     A) internal energy.

 

     B) thermal energy.

 

     C) temperature.      Answer   Temperature (in K) of a gas is defined as the average kinetic energy of the molecules

 

     D) heat.

 

10.  The internal energy of an ideal gas depends on

 

       A) its volume.

 

       B) its pressure.

 

       C) its temperature.      Answer    U = 3/2 nRT    so depends only on temperature and number of moles

 

       D) all of the above

 

11.  The reason ocean temperatures do not vary drastically is that

 

       A) water has a relatively high rate of heat conduction.

 

       B) water is a good radiator.

 

       C) water has a relatively high specific heat.      Answer

 

       D) water is a poor heat conductor.

 

12.  The heat required to change a substance from the solid to liquid state is referred to as

        the  

 

       A) heat of fusion.      Answer   definition

 

       B) heat of vaporization.

 

       C) heat of melting.

 

       D) heat of freezing.

 

13.  The heat required to change a substance from  liquid to the vapor state is referred to as the  

 

       A) heat of fusion.

 

       B) heat of vaporization.      Answer  definition

 

       C) heat of evaporation.

 

       D) heat of condensation.

 

14.  In a cloud formation, water vapor condenses into water droplets which get bigger and

       bigger until it rains.  This will cause the temperature of the air in the clouds to

 

       A) increase.      Answer         The temp change (up) goes into the air

 

       B) decrease.

 

       C) stay constant.

 

       D) freeze.

 

15.  By what primary heat transfer mechanism does one end of an iron bar become hot when

        the other end is placed in a flame?

 

       A) natural convection

 

       B) conduction      Answer  definition

 

       C) radiation

 

       D) forced convection

 

16.  The process whereby heat flows by the mass movement of molecules from one place to

       another is referred to as  

 

       A) conduction.

 

       B) convection.      Answer    definition

 

       C) radiation.

 

       D) inversion.

 

17.  By what primary heat transfer mechanism is a pot of water heated on a stove?

 

       A) convection      Answer definition and this example also explained in the text

 

       B) conduction

 

       C) radiation

 

       D) all of the above in combination

 

18. A ball of mass M and speed v collides head-on with a       ball of mass 2M and speed v/2 as shown on the right. If       the two balls stick together, their speed after the collision       is         A) 0                       Answer      Conservation Law  Mv - 2Mv/2 = 0, so v = 0 after         B) v/2         C) (2)1/2v/2         D) (3)1/2v/2         E) 3v/2

 

19. A ball is thrown straight up by a student who is at rest on the surface of the Earth. A graph of

      the position y as a function time t is shown below. For ease in calculations assume g = - 10

      m/s² in all calculations for this problem. Parts a through d are included in this problem.

 

a. At which of the following times is the     ball farthest from the student?       1) 1 s       2) 2 s       3) 3 s     Answer   y is greatest there       4) 4 s       5) 5 s

    b. At which of the following times is the speed of the ball the least?

 

       1) 1 s

 

       2) 2 s

 

       3) 3 s     Answer      definition of speed as delta y over delta time

 

       4) 4 s

 

       5) 5 s

 

    c. Which of the following best describe the acceleration of the ball?

 

       1) It is downward and constant from 0 to 6 s     Answer    acceleration of gravity is downward and constant

 

       2) It is downward and increases in magnitude from 0 to 3 s then decreases

 

       3) It is downward and decreases in magnitude from 0 to 3 s then increases

 

       4) It is upward and increases in magnitude from 0 to 3 s then decreases

 

       5) It is upward and decreases in magnitude from 0 to 3 s then increases

 

    d. What is the initial speed of the ball?

 

       1) 30 m/s      Answer    y = y_o + v_ot + 1/2at2     ð  0 = 0 + 6v_o + 1/2)(10)6²   ð  6v_o = 5(36)  ð  v_o = 30 m/s

 

       2) 45 m/s

 

       3) 60 m/s

 

       4) 90 m/s

 

       5) 180 m/s

 

 

Part 2

Problems: Show all Work

 

1.  Assume that the coefficient of linear expansion of a metal rod, originally 100 m long

     at 20^o C, is (17x10^-6 C^o)^-1 at 20^o  C. What will be the expansion of the rod if the

     temperature rises to 30^o C? Show the final answer with units - a calculator is not

     necessary.

 

DL = aL₀DT = (17x10^-6 C^o)^-1 (100)(30 - 20) = = (17x10^-6 C^o)^-1 (1000)

= 1x10³/17x10⁶) = 1x10^-3 m

 

 

2. Assume that the specific heat of a piece of metal is 450 J/kg·C at 20^o C. How much

    heat is required to raise the temperature of 10 kg of the metal from 20^o C to 30^o C?   

    Give the exact answer along with units

 

Q = mcDT = (10 kg) (450 J/kg·C)( 30^o C - 20^o C)= 45,000 J or 45 kJ

 

3.  Assume that a glass window in a house is 2 m x 2 m and 5 mm thick. The

     temperature inside the house (of the side of the pane inside the house) is 13

     degrees centigrade and the temperature of the outside (of the side of the pane that is

     outside the house) is 12 degrees centigrade.  The thermal conductivity of the glass is

     0.84 J/s·m·C. What is the rate of heat flow through the glass? For this problem leave

     the answer as an expression with the numbers inserted along with units for the final

     answer.

 

We use the empirical relationship       show units means show units - not tied up in the individual components

 

Q/t = kADT/l

 

where Q is heat, k is the thermal conductivity, A is the cross sectional area and l is the distance travelled (distance between the two sides).

 

A = 2mx2m = 4 m², l = 5x10^-3 m, k =  0.84 J/s·m·C, DT = 13 -12 = 1 C^o

 

Q/t = kADT/l = k =  (0.84 J/s·m·C)(4 m2)(1)/ 5x10^-3 m J/s

 

4.  An automobile tire has an absolute pressure (gauge plus atmospheric) of 300 kPa at

     a temperature of 10 degrees C. After a trip, the temperature within the tire rises to 40

     degrees C. Assume there is no change in the volume of the tire. What is the absolute

     pressure within the tire now?  Specific number not required, just insert values and

     provide units for the answer.              show units means show units - not tied up in the individual components

 

We use the ideal gas law before and after - using K for temperature

10 degrees C = 283 K       40 degrees C = 313 K

 

P₁V₁ = nRT₁    P₂V₂= nRT₂   ð  P₁/T₁ = nR       P₂/T₂ = nR   ð  P₁/T₁ =  P₂/T₂

 

P₂ = P₁(T₂/T₁)  =  (3.0x10⁵ Pa)(313 K)/283 k Pa

 

Part 3

Extra Credit

 

Match the description on the left with the person on the right. For example, if item 1 is attributed to person a, then place the letter a in the blank beside item 1 labeled Ltr

 

Description	Ltr	Person
1. F = Gm1m2/R2	b	a. Claussius
2. Equivalence of mechanical and heat energy	d	b. Newton
3. Hypothesis concerning number of molecules	e	c. Boyle
4. Relationship between pressure and volume	c	d. Joule
5. R/NA	g	e. Avogadro
		f. Carnot
		g. Boltzmann