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PHYS 212 Examination 1
Name (print): _____________________________
Signature _____________________________
Problem 1 __________________
Problem 2 __________________
Problem 3 __________________
Problem 4 __________________
Problem 5 __________________
Problem 6 __________________
Total __________________
Directions: This exam contains six problems worth 20 points each for a possible 120/ points. Your solutions should be written as neatly as possible and arranged in a logical manner. Credit will be awarded on the basis of thought, compactness, and neatness of the written solution. Remember to use basic physical principles in solving the problems. Show all of your work. I will not award full points for a problem with a solution that I am unable to decipher even if the answer is correct.
An equation sheet has been provided. CRC handbooks are allowed. Calculator rule is in effect. Good Luck!
Problem 1. A copper slug having a mass of 75 grams is heated to a temperature of 312^0 C. The slug is dropped into a beaker containing 220 grams of water. The initial temperature of the water and beaker is 12^0 C. What is the final equilibrium temperature of the system? (Hint: heat capacity C, is not the same as specific heat which is heat capacity per unit mass)
Note: Cbeaker = 45 cal/K (heat capacity) , cwater = 1.00 cal/g ⋅⋅ K, ccopper = 0.0923 cal/g ⋅⋅ K
− m (^) Cu cCu ∆ T = mwcw ∆ T + Cbea ker∆ T
mCu cCu ( T − Tf ) = mwcw ( T f − Ti ) + Cbea ker( T f − Ti )
Cu Cu bea w w
Cu Cu bea i w w i f (^) m c C m c
m c T C T mc T T
ker
ker
cal g K g cal K cal g K g
cal g K g C cal K C cal g K g C T (^) f ⋅ + + ⋅
C
cal C
cal T (^) f 0 200
- 9 /
Problem 3.
- The surface of the sun has a temperature of about 5800K. If the radius of the sun is 6.96 × 108 m, calculate the total energy radiated by the sun each day. Assume that the sun has an emissivity of unity.
P AeT P ( W m K ) ( m ) ( )( K ) 4 26 J s 4 8 2 4 8 2
- 6696 10 4 6. (^9610) 15800 = 3. 9 × 10
= σ ∴ = × −^ ⋅ ^ π ×
( 3. 9 × 10 26 J s )( 86400 sday ) = 3. 4 × 1031 J!
- A wall of a house whose face area, A , is 100 ft^2 , is made up of 4 inch bricks (R = 4.00 ft^2 ⋅F^0 ⋅h/BTU), a thin dead air space (R = 0.17 ft^2 ⋅F^0 ⋅h/BTU), 0.5 inches of sheathing (R = 1.32 ft^2 ⋅F^0 ⋅h/BTU), fiberglass insulation 3.5 inches thick (R = 10. ft^2 ⋅F^0 ⋅h/BTU) and 0.5 inches of drywall (R = 0.45 ft^2 ⋅F^0 ⋅h/BTU). If the outside temperature on a cold day is 15^0 F and the inside temperature is 68^0 F, what is the rate of heat transfer through the wall? In Idaho, where surface mounted evaporators are only about 10% efficient at temperatures below 25^0 F, how much power, in watts, would the compressor of a heat pump have to develop to compensate for this energy loss? Note: 1 Btu = 1055 J .
∑
−
i
Ri
T T H A^21
( )
BTU hr ft F hBTU
H ft F F 315
- 00 0. 17 1. 32 10. 90 0. 45
100 68 15 2 0
2 0 0
−
W BTU
J s
hr hr
BTU
- 3 1
1055 3600
1 1
315 × × =
. 9 × 92. 3 W = 83 W
Problem 4. How much heat is needed to take ice of mass 720 grams at –10^0 C to a liquid state at 15^0 C?
cice = 2220 J/kg ⋅ K cw = 4190 J/kg ⋅ K Lf = 333 kJ/kg
Q 1 (^) = mc ∆ T =( 0. 720 kg )( 2220 J / kg ⋅ K )( 100 C )= 15. 98 kJ ice @ -10^0 C to ice @ 0^0 C Q (^) 2 = mLf =( 0. 720 kg )( 333 kJ / kg )= 239. 8 kJ ice @ 0^0 C to water @ 0^0 C Q (^) 3 = mc ∆ T =( 0. 720 kg )( 4190 J / kg ⋅ K )( 150 C )= 45. 25 kJ water @ 0^0 C to water @ 15^0 C
Q 1 (^) + Q 2 + Q 3 = 300 kJ
If we supply the ice with a total heat of only 210 kJ, what is the final state of the system?
kg kJ kg
kJ L
Q
m f
leftover
- 580 333 /
580 grams of water and 140 grams of ice.
( )^2
3
cos
ax y
qQ xdy
dF dFx dF
( )
∫
a
a
x
ax y
qQ xdy
F F
2 2 2 3
i
x x a
qQ
Fnet ˆ
4 0 2 +^2
r
Problem 6. With the aid of PV diagrams, explain the Otto cycle heat engine.
Otto Cycle Gasoline Engines
- During the intake stroke (O → A), air at atmospheric pressure is drawn into the cylinder and the volume increases @ atmospheric pressure from V 2 to V 1 (isobaric).
- During the compression stroke (A → B), the fuel-air mixture is compressed adiabatically from volume V 1 to volume V 2 , and the temperature increases from TA to TB. The work done on the gas is the area under the AB curve.
- Combustion occurs in the process B → C and heat QH is added to the gas. This heat is not from the outside of the system. It is heat released during the combustion process. During this process the pressure and temperature increase rapidly but the volume remains essentially constant (isovolumetric). No work is done on the gas.
- During the power stroke (C → D), the gas expands adiabatically from V 2 to V 1 , causing the temperature to drop from TC to TD. The work done by the gas is the area under the CD curve.
- In the process D → A, heat QC is extracted from the gas as its pressure decreases at constant volume (hot gas is replaced by cool gas). No work is done during this process.
- During the exhaust stroke (A → O), the residual gases are exhausted at atmospheric pressure and the volume decreases from V 1 to V 2 (isobaric).
P
V
A
B
D
C
Qh
Qc
O
V 2 V 1
