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Thermo Notes

1. An Asian elephant weighs 8818.4 pounds. Its mass in standard conditions is 8818.4 lb, in kilograms is 4000 kg, and in slugs is 274.0847 slugs. 2. A mass of 0.065 kg needs to accelerate at a rate of 0.32 m/s^2. The required force is 0.021 Newtons. 3. An airplane with a mass of 12 tons at sea level has a mass of 24,000 pounds. Its mass in slugs is 745.94 slugs and in kilograms is 10,886 kg. At an elevation of 40,000 feet, its gravitational weight in pounds is 23,760

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0% found this document useful (0 votes)
207 views16 pages

Thermo Notes

1. An Asian elephant weighs 8818.4 pounds. Its mass in standard conditions is 8818.4 lb, in kilograms is 4000 kg, and in slugs is 274.0847 slugs. 2. A mass of 0.065 kg needs to accelerate at a rate of 0.32 m/s^2. The required force is 0.021 Newtons. 3. An airplane with a mass of 12 tons at sea level has a mass of 24,000 pounds. Its mass in slugs is 745.94 slugs and in kilograms is 10,886 kg. At an elevation of 40,000 feet, its gravitational weight in pounds is 23,760

Uploaded by

jecuadrante
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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IDEAL GAS

1. What will be the resulting pressure if the air is three pound at 25psi and 15O° C is
heated at constant volume of 30O0 F .
Solution:
p1 p2
=
T1 T2
25psi v2
=
15O0 C + 460K 30O0 F + 460K
Final Answer:

P2 = 31.15psi

2. A 3.3 liters of an ideal gas is contained at 6.6atm and 25°C. How many moles of
this gas are present?

Solution:

PV nRT
PV = nRT =
RT RT
T = °𝐶 + 273K
T = 250 C + 273K
PV
T = 298K 𝑛=
RT

(6.6 𝑎𝑡𝑚)(3.3 𝑙𝑖𝑡𝑒𝑟𝑠)


𝐿 × 𝑎𝑡𝑚
(0.0821 𝑚𝑜𝑙 × 𝐿 ) (298𝐾)

Final Answer:

N= 0.890mol
3. A hot air balloon has a constant pressure of 600kPa and 250°𝐶. How many
moles of air must be put into the balloon for 250KJ of work to be done on the
balloon?

Solution:

PV nRT
=
RT RT

𝑃𝑉 𝑊
𝑛 = 𝑅𝑇 𝑜𝑟 𝑛 = 𝑅𝑇

T = °𝐶 + 273𝐾
T = 250°𝐶 + 273K
T = 523K

Final Answer:

n = 0.057mol

4. A scuba diver carries a tank 10 liters of air at a pressure of 3atm. If the


temperature remains constant, what will be the final volume of the air if the
pressure is reduce to 2atm?

Solution: Final answer:


V1 = 10L P1 v1 = P2 V2
(𝑃1 )(𝑉1 ) V2 = 15L
P1 = 3atm V2 = 𝑃2

3 𝑎𝑡𝑚 (10𝐿)
P2 = 2atm1 V2 = 2 𝑎𝑡𝑚

V2 =?
5. A sample gas at a temperature of 20°C occupies a volume of 5 liters and as
a pressure of 2 atmospheres. Wat will be the new pressure of if the volume
is reducing to 2 liters while keeping the temperature constant?

Solution: Final answer:


V1 = 5L P1 v1 = P2 V2
(𝑃1 )(𝑉1 )
P1 = 2atm P2 = PP22==5L5L
𝑉2

2 𝑎𝑡𝑚 (5𝐿)
V2 = 2L V2 =
2 𝑎𝑡𝑚

P2 =?

6. A balloon is filled with 2 moles of helium gas at a pressure of 1 atmosphere and a


temperature of 25°C. If the balloon is heated to 50°C while keeping the volume
constant, what will be the new pressure inside the balloon?

Solution:

P1 = 1atm T1 = 25°C + 273.15

T1 = 25°C T1 = 298.15K
K°C
T2 = 50°C T2 = 50°C + 273.15

P2 =? T2 = 323.15K
K°C

P1 P
= T2 Final answer:
T1 2

𝑃 1 𝑇2
P2 = P2 = 1.08atm
𝑇1

1𝑎𝑡𝑚 (323.15𝐾)
P2 =
298.15𝐾
7. A sample of gas has a pressure of 3 atmosphere and occupies a volume of 2
liters at a temperature of 25°C. If the temperature is increased to 100°C while
keeping the volume constant, what will be the new pressure?
Solution:
P1 = 3atm T1 = 25 + 273.15
T1 = 25°C T1 = 298.15K
K°C
T2 = 100°C T2 = 100°C + 273.15
P2 =? T2 = 373.15K
K°C
𝑃1 𝑃
= 𝑇2 Final answer:
𝑇1 2

𝑃1𝑇2
P2 = 𝑇1 P2 = 3.75atm
3 𝑎𝑡𝑚 (373.15𝐾)
P2 = 298.15𝐾

8. During a polytropic process, 10 lb of an ideal gas, whose R= 40 ft-lb/lb-⁰R and C


Cp=0.25 btu/lb-⁰R changes state from 20 psia and 40°F to 120 psia and 340°F.
Determine: (a) n, (b) AU and AH. (c) AS, (d) Q, (e) work non-flow, (f) work steady
flow.

Given:
P1 = 20 psia m = 10 lb
P2 = 120 psia R = 40 ft-lb/lb °f
𝐵𝑡𝑢
T1 = 40 + 460 = 500 °R Cf = 0.25 𝑙𝑏− °R

T2 = 340 + 460 = 800 °R


Solution:
40
a.) n b.) 𝐶𝑣 = 𝐶𝑝 − 𝑅 = 0.25 − 778

𝑝2 𝑛−1 𝑡2 𝑏𝑡𝑢
[ ] = 𝐶𝑣 = 0.1986 𝑙𝑏−𝑟
𝑝1 𝑛 𝑡1

120 𝑛−1 800


( 20 ) = Δ𝑢 = 𝑚𝑐𝑣 (T2 – T1)
𝑛 500
= (10) (0.1956) (800-500)
𝑛−1
( ) 𝐼𝑛 6 = 𝐼𝑛 1.6 Δ𝑢 = 595 − 8 𝑏𝑡𝑢
𝑛
𝑛−1 0.4700
= Δ + 1 = 𝑚𝑐𝑝 (T2 – T1)
𝑛 1.7918
= 10 (0.25) (800-500)
n = 1.356 Δ𝐻 = 750 𝐵𝑡𝑢
MASS, WEIGHT, AND FORCE
1. An Asian elephant weighs 8818.4
pounds, what is its (A) mass at
standard condition, (B) mass in
kilogram and (C) mass in slugs? 2. Calculate the force in Newton’s,
GIVEN: needed to accelerate 65gram mass
𝑐𝑚
at a rate of 32 𝑠 2 .
w = 8818.4lbs
𝑓𝑡
g = 32.174𝑠 2 GIVEN:

RER’D: m = 65g
𝑐𝑚
A = mass at standard condition d = 32 𝑠 2

B = mass in Kg REQ’D:

C = mass in slugs Force in Newton’s

SOLUTION: SOLUTION:
𝐹𝑔𝐾 1𝑘𝑔
(A) m= 65𝑔 × = 0.065kg
𝑔 1000𝑔
𝑐𝑚 1𝑚 𝑚
(8818.4𝑙𝑏𝑓)(32.174
𝑙𝑏𝑚 𝑓𝑡
∗ ) 32 𝑠 2 × = 0.32𝑠 2
𝑙𝑏𝑓 𝑠2 100𝑐𝑚
m= 𝑓𝑡
32.174 2
𝑠 𝑚
0.32
𝑚 𝑠2
m = 8818.4lbm F = ma= (0.065kg)( 0.32𝑠 2)
𝑚
0.32
(B) 8818.4lbm × 2.2046𝑙𝑏𝑚
1𝑘𝑔
F = 0.021 N 𝑠2

m = 4000kg

1𝑠𝑙𝑢𝑔
(C) 8818.4lbm × 82.174𝑙𝑏𝑚

m = 274.0847 slug
3. The mass of a given airplane at SOLUTION:
sea level (g= 32.1 fps²) is 12 2000 𝑙𝑏𝑚
tons. Find its mass in pounds, (A) m = 12 tons × 1 𝑡𝑜𝑛𝑠
slugs, and kg and its gravitational
weight in pounds when it's
travelling at a 40 000ft elevation. m = 24 000lbm
The acceleration of gravity 𝑚
decreases by 3.33x10 raise to 0.32 1 𝑠𝑙𝑢𝑔
𝑠2 ×
(B) m = 24 000lbm 32.174 𝑙𝑏𝑚
negative 6 for each foot of
𝑚
elevation. 0.32
m = 745.94 slugs
𝑠2
GIVEN: 𝑚
0.32 2 1𝑘𝑔
𝑠
(C) m = 24 000lbm ×
m = 12 tons 2.205 𝑙𝑏𝑚
𝑚
g = 32.1 fps 2 0.32 2
m = 𝑠10884.35kg
REQ’D: 𝑚
0.32
𝑠2
A = MASS IN POUNDS
𝑚 – (3.33 × 10 )(h)
-6
(D) g40000 = gs∙L
B = MAS IN SLUGS 0.32
𝑠2 𝑓𝑝𝑠 2
= 32.9 fps2 – (3.33 × 10-6 ) (40 000ft)
𝑓𝑡
C = MASS IN KILOGRAM
g40 000 = 31.9668 fps2
D = GRAVITATIONAL WEIGHT
IN POUNDS 𝑚𝑔 (745.94 𝑠𝑙𝑢𝑔)(31.9335 𝑓𝑝𝑠 2 )
w= = 𝑠𝑙𝑢𝑔−𝑓𝑡
𝑘 1
𝑙𝑏𝑓− 𝑠2

w = 23 320.47 lbf
𝑚
0.32
𝑠2
𝑚
0.32
𝑠2
4. What is the mass in grams and SOLUTION:
the weight in dynes and in gram- 1𝑙𝑏𝑚 1𝑘𝑔 1000𝑔
force of 18oz salt? local g is 9.65 (A) m = 18𝑜𝑧 × × ×
16𝑜𝑧 2.205𝑙𝑏𝑚 1𝑘𝑔
m/s² and 1lbm = 16 oz.
m = 510.20 𝑔
GIVEN: 𝑚
m = 18oz 0.32
𝑠2 𝑚 100𝑐𝑚
𝑚 𝑚𝑔 (510.20𝑔)(9.65 2 )( )
g = 9.65𝑠 2 (B) w = = 𝑚 𝑔∙𝑐𝑚
𝑠 1𝑚
𝑘 0.32 1
𝑑𝑦𝑛𝑒∙𝑠2
1lbm = 16oz 𝑠2

REQ’D: w = 492 343 dyne


A = MASS IN GRAMS 𝑚
0.32
𝑠2
(510.20𝑔)(9.65 2 )
𝑐𝑚
B = WEIGHT IN DYNES 𝑚𝑔 𝑠
(C) w = = 𝑚 𝑔𝑚 𝑐𝑚
𝑘 980.66 ∙
0.32 𝑔𝑓 𝑠2
C = WEIGHT IN GRAM-FORCE 𝑠2
w = 502.05gf
𝑚
0.32
𝑠2
𝑚
0.32
𝑠2
CONSERVATION OF MASS
1. A fluid moves in a steady flow SOLUTION:
manner between two sections in
(A) ṁ = P1 A1 V1 = P2 A2 V2
a flow line. At Section 1: a₁ = 12 1𝑙𝑏 𝑓𝑡
ft², v₁ = 50 ft/m, v₁ = 4 ft³ / lb. At = (4𝑓𝑡 2 ) (12𝑓𝑡) (50 𝑚𝑖𝑛)
Section 2: a2 = 3 ft², p₂ = (B) ṁ = P2 A2 V2
0.10lb/ft³. 𝑙𝑏
ṁ 150
𝑚𝑖𝑛
v2 = 𝑃 𝐴 = 𝑙𝑏
CALCULATE: 2 2 (0.10 2 )(3𝑓𝑡 2 )
𝑓𝑡

(A) the mass flow rate. FINAL ANSWERS:


(B) the speed at section 2.
(A) 𝑙𝑏
ṁ = 150𝑚𝑖𝑛
GIVEN:
A1 = 12 ft2
𝑓𝑡 3 𝑓𝑡
V1 = 4 (B) v = 500𝑚𝑖𝑛
𝑙𝑏
𝑓𝑡
v1 = 50 𝑚
𝑙𝑏
A2 = 3 ft3 P2 = 𝑓𝑡 3

2. If pump discharges 68gpm of SOLUTION:


water whose specific weight is 𝑄४k
52.5lb/ft³ (g = 32.174ft/s²), (A) ṁ = 𝑔

FIND: 𝑔𝑎𝑙 1𝑓𝑡2 𝑙𝑏𝑓 𝑙𝑏𝑚 𝑓𝑡


(68 )( )(52.5 3 )(32.174 ∙ )
𝑚𝑖𝑛 7.481𝑔𝑎𝑙 𝑓𝑡 𝑙𝑏𝑓 𝑠2
(A) the mass flow rate in lb/min. ṁ= 𝑓𝑡
32.174 2
(B) the total time required to fill a 𝑠

vertical cylinder tank 8ft in 𝑙𝑏


diameter and 15ft in height. ṁ = 477.209𝑚𝑖𝑛
GIVEN:
𝜋𝑑2 ℎ 𝜋 (8)2(15)
Q = 65gpm (B) v = =
𝑙𝑏 4 4
४ =52.5 = 753.98ft2
𝑓𝑡 3
𝑓𝑡
g = 32.174 𝑠 2 𝑣 𝑣 753.98𝑓𝑡 3
Q=𝑡 xt=𝑄 = 𝑔𝑎𝑙 1𝑓𝑡3
d = 8ft (68 )( )
𝑚𝑖𝑛 7.481𝑔𝑎𝑙

h = 15ft
t = 83min
3. Air enters steadily at 5.21 kg/m³
and 35 m/s. What is the mass
SOLUTION:
flow rate through the nozzle if the
inlet area of the nozzle is 85 cm²? ṁ = pAv
GIVEN: 𝑘𝑔
= (5.21𝑚3 ) ( 85𝑐𝑚2 ) (100𝑐𝑚 )2 (35 𝑠 )
1𝑚 𝑚

𝑘𝑔
P = 5.21𝑚3 𝑘𝑔 1𝑚 2 𝑚
𝑚 = (5.21𝑚3 ) ( 85𝑐𝑚2 ) (100𝑐𝑚 ) (35 𝑠 )
v = 35 𝑠
A = 85𝑐𝑚2 FINAL ANSWER:
REQ’D: 𝑘𝑔
ṁ = 1.55
(A) = MASS FLOW RATE 𝑠

SOLUTION:
(A)
4. Two gaseous streams enter a 𝑙𝑏 1 𝑓𝑡
ṁ = P2 A2 V2 = (0.10𝑓𝑡 3 ) (60in²) (12 𝑖𝑛)2 v2
combining tube and leave as a
v2 = P2 A2 ṁ2
single mixture. These data apply
𝑙𝑏 1𝑓𝑡 2 𝑙𝑏
at the entrance section: = (0.10𝑓𝑡 3 ) (60in²)(144 𝑖𝑛2 )(16.67 𝑠 )

GAS 1: a, = 70 in², v₁ = 400 fps; v₁ =


𝑓𝑡
12 ft³/lbm v2 = 0.69 𝑠
GAS 2: a₂ = 60 in², mass flow rate 2
= 16.67 1b/s p₂ = 0.10 lb/ft³
AT EXIT: V3= 300 fps, v3 = 6ft³/lb (B) ṁ3 = ṁ1 + ṁ2
FIND:
𝐴1 𝑉1
ṁ1 =
A) the speed V2 at section 2. 𝑣1

1𝑓𝑡
B.) the flow and area at exit section. (70𝑖𝑛 2 )( )(400 𝑓𝑝𝑠)
12𝑖𝑛
= 𝑓𝑡3
12
GIVEN: 𝑙𝑏𝑚

𝑙𝑏
A1 = 70 𝑖𝑛2 ṁ1 = 16.20 𝑠
V1 = 400 fps 𝑙𝑏 𝑙𝑏
𝑓𝑡 3 ṁ3 = 16.20 𝑠 + 16.67 𝑠
v1 = 12𝑙𝑏𝑚
A2 = 60𝑖𝑛2 𝑙𝑏
𝒍𝒃𝒎
ṁ3 = 32.87 𝑠
ṁ 2 = 16.67 𝒔
𝒍𝒃𝒎 𝐴3𝑉3 𝑙𝑏 𝐴3 (300𝑓𝑝𝑠)
P2 = 0.10 𝒇𝒕𝟑 ṁ3 = = 32.87 𝑠 = 𝑓𝑡3
𝑣3 6
𝑙𝑏
V3 = 300fps
𝑓𝑡 3
v3 = 6𝑙𝑏𝑚 32.87 50𝐴3
= = A3 = 0.6574ft2
50 50
CONSERVATION OF ENERGY

1.) A reversible non-flow constant volume process decreases the internal energy by
316.5 kJ for 2268 kg of a gas for which =430 J/ kg-k and k = 1.35 For the process,
determine: (a) Non-flow Work, (b) Heat, (c) All, (d) AH, and (e) The change of
entropy if the initial temperature is 204.4°C

Solution:

a.) Non-flow Work d.) Δ 𝐻


Wn = 0 Δ𝐻 = mcp (T2 – T1)
b.) Heat = 2.268 (1.65857) (363.012 – 479.4)
Q = mcn (T2 – T2) Δ𝐻 = 427.28 𝑘𝑗
𝑇2
= - 316.5 ks e.) Δ 𝑆 = 𝑚𝑐𝑣 𝐼𝑛 𝑇1

363.812
c.) Δ𝑢 = 2.268 × 1.122857) 𝐼𝑛 ( )
477.4
𝑟 430
𝑐𝑣 = 𝑘−1 = 1.35−1
Δ𝑢 – mcv ( T2 – T1)
= (2.268 × 1.22857) (369.81 − 477.4)
Δ𝑢 = −361.5 𝑘𝑗

2.) 8 lbs of air drops from 80 psia to 5 psig. For an internally isothermal reversible
process at 88°F, determine: (a) non-flow work, (b) Steady flow work, (c) 0. (d)
Alf and AH, and (e) AS.

Given:
T = 88 + 460 = 540 °R
m = 81 lb
P1 = 80 psia
P2 = 5 + 14.7 = 19.7 psia

Solution:

a.) Non-flow work d.) Δ𝑉 = 0


𝑣2 𝑝1
∫ 𝑝𝑑𝑣 = 𝑝1 𝑣1 , 𝐼𝑛 𝑣1
= 𝑚𝑅𝑇 𝐼𝑛 𝑝2
Δ𝐻 = 0
(8)(53.34)(54.8) 80
= 𝐼𝑛
728 19.7

𝑄
𝑤𝑛 = 421.2 𝐵𝑡𝑢 e.) Δ𝑆 =
𝑇
421.2
= 548
b.) Steady flow-work
𝑣2 𝐵𝑡𝑢
∫ 𝑉𝑑𝑝 − 𝑝1 𝑣1 𝐼𝑛 𝑣1 = 0.7686 ( °R )
= 421.1 𝐵𝑡𝑢

c.) Q = Δ𝑣 + 𝑊𝑛
= 421.2 𝐵𝑡𝑢
𝐵𝑡𝑢
3.) Steam enters turbine with an enthalpy of 1292 and leaves an enthalpy of
𝑙𝑏
𝐵𝑡𝑢 𝐵𝑡𝑢 𝐵𝑡𝑢
1098 , Transferred Heat is 13 . What is the work in 𝑚𝑖𝑛 and hp per a flow
𝑙𝑏 𝑙𝑏
𝑙𝑏
of 2 𝑠𝑒𝑐?

𝐵𝑡𝑢 𝐵𝑡𝑢
Given: h11 = 1292 h2 = 1098
𝑙𝑏 𝑙𝑏
𝐵𝑡𝑢 𝑙𝑏
a = 13 flow = 2 𝑠𝑒𝑐
𝑙𝑏

Solution:

h1 – a = h2 + w
w = h1 – (h2+9)
𝐵𝑡𝑢 𝐵𝑡𝑢 𝐵𝑡𝑢
w = 1292 – [ (1098 ) + 13 ]
𝑙𝑏 𝑙𝑏 𝑙𝑏
𝐵𝑡𝑢 2𝑙𝑏 1 ℎ𝑝
w = 181 x 𝑠𝑒𝑐 x 𝐵𝑡𝑢
𝑙𝑏 4.24
𝑙𝑏

w= 512.264 hp

𝐾𝑔
4.)An air compressor receives 272 𝑚𝑖𝑛 . of air at 99.29 kPaa and a specific

volume of 0.026 𝑘𝑔 . The air flows steady the compressor and is discharged at
m³ 𝐽
689.5 kPaa and 0.0051 𝑘𝑔 . The initial internal energy of the air is 1594 𝑘𝑔 ; at
𝐽
discharge, the internal energy is 6241 𝑘𝑔 . The compressor rejects heat at
𝐽
4383 𝑘𝑔 . The change in kinetic energy is 896 J/kg increase. Compute the work
in kW.

𝐾𝑔
Given: p1 = 99.29 kPa m = 272 𝑚𝑖𝑛

v1 = 0.026 𝑘𝑔 p2 = 689.5 kPa
𝐽 m³
u1 = 1594 𝑘𝑔 v2 = 0.0051 𝑘𝑔
𝐽 𝐽
Q = -4363 𝑘𝑔 u2 = 6241 𝑘𝑔
𝐽
Δk = 896 𝑘𝑔
Solution:
w ? Q = P1 + K1 + Wf1 + V1 + Q = P2 + K2 + Wf2 + U2 + W
K1 K2 Basis 1Kgm
Wf1 Wf2 m³
Wf1 = P1 V1 = [99.29 KN/m2] [ 0.026 ]
𝑘𝑔
U1 energy diagram. U2 𝐾𝐽
= 2583 𝑘𝑔
Wf2 = P2 V2 = [689.5 Kn/m2]
𝐾𝐽
= 3.516 𝑘𝑔
Wf1 + V1 + Q = ΔK = Wf2 + V2 + W
= 2.582 = 1. 594 – 4. 383 = 0.896 + 3.156 + 6.241 + W
𝐾𝐽
W = -10.86 𝑘𝑔
𝐾𝐽 𝑘𝑔
W = [-10.86 𝑘𝑔 ] [ 272 𝑚𝑖𝑛 ]

𝐾𝐽
W= -2954 𝑚𝑖𝑛
5. A 50kg block is released from its resting position at a height of 10m from the
ground. If we neglect air resistance, what is the block's total energy at a
height of 4m from the ground.

GIVEN:
m = 50kg
h = 10m

SOLUTION:
PE = mgh
𝑚
= (50kg) (9.8𝑠 2) (10m)
= 4900J

FINAL ANSWER:
PE = 4.9kJ

6. Problem: A spring with a spring constant of 500 N/m is compressed by 0.1


meters. Assuming no energy losses due to friction, what will be the maximum
potential energy stored in the spring when it is released?

GIVEN:
𝑁
k = 500 𝑚
x = 0.1m

SOLUTION:
1
PE = 2k𝑥 2
1 𝑁
PE = 2 (500𝑚) (0.1m)2

FINAL ANSWER:
PE = 2.5kJ

7. A 0.25kg rubber ball is released from a height of 10m and is allowed to


bounce repeatedly. Each time the ball strikes the ground, ten percent of the
ball's kinetic energy is lost in the collision. What is the maximum height the
ball will reach after hitting the ground four times?

GIVEN: m = 0.25kg h = 10m


10% of kinetic energy lost, the ball has 90% of its previous potential energy at
the top of its flight.

SOLUTION: FINAL ANSWER: PE = 45.5J


PE = mgh
𝑚
= (0.25kg) (9.8𝑠 2) (10m) 𝑃𝐸4 = 16.1J = mg ℎ4
𝑃𝐸4
SOLUTION: ℎ4 = 𝑚𝑔
90% 16.6𝐽
= 0.9 ℎ4 = 𝑚
100 (0.25𝑘𝑔)(9.8 2 )
𝑠
𝐾𝐸4 = (24.5) (0.9)4
FINAL ANSWER: ℎ4 = 6.6m
KE = 16.1J
8. A roller coaster of mass 500kg is at its highest point in a loop traveling at a
velocity of 4ms. The loop is 15 meters tall. Assuming 5000J of energy is lost
between the highest and lowest points of the loop, how fast is the roller
coaster traveling when it reaches the lowest point of the loop?

GIVEN:
m = 500kg
𝑚
V1 = 4 𝑠
h = 10m and F = 500J
SOLUTION: FINAL ANSWER:
PE1 + KE1 = PE2 + KE2 + F
𝑚
PE1 + KE1 – F = KE2 V2 = 12.2𝑠 2
1 1
Mgh + 2 𝑚𝑣12 – F = 2 𝑚𝑣22
2f
V2 = 2 gh  V12 
m
m m 2(500 J )
2(9.8 2
(15m)  (9 )2 
s s 500kg
DENSITY

1. A reservoir of glycerin has a mass of 1,200 kg and a volume of 0.952 cm³ Find
the density.

GIVEN: FINAL ANSWER:


m = 1200kg
𝑘𝑔
v = 0.952m2 𝜌 = 1260.5 𝑚3
SOLUTION:
𝑚
𝜌= 𝑣
1200𝑘𝑔
=
0.952𝑚 3
2. Calculate the density of an object with a mass of 112 g and a volume of 9.98cm³

GIVEN:
m = 112g
v = 9.98cm3 FINAL ANSWER:
SOLUTION:
𝑚 𝑔
𝜌= 𝑣 𝜌 = 11.2 𝑚3
112𝑔
= 9.98𝑚3

3. A certain gas occupies a volume of 0.28 m³ and has a mass of 0.40 kg. What is
the density of the gas?

GIVEN: m = 0.40kg
v = 0.28m3 FINAL ANSWER:
SOLUTION:
𝑚 𝑘𝑔
𝜌= 𝑣 𝜌 = 1.42 𝑚3
0.40𝑘𝑔
= 0.28𝑚3
4. A certain gas fills a 3 Liter balloon and has a mass of 0.1 kg. What is the density
of the gas?

GIVEN:
m = 0.1kg FINAL ANSWER:
v = 3L
𝑘𝑔
SOLUTION: 𝜌 = 0.033 𝐿
𝑚
𝜌= 𝑣
0.1𝑘𝑔
= 3𝐿
TEMPERATURE

1. Define a new temperature scale, say "N, in which the boiling and freezing point are
1000°N and 100°N, respectively, and correlate this scale with the Fahrenheit and
Celsius scales. What is the absolute temperature at "N?

SOLUTION: by absolute zero temperature


= -121 °f
BP 100℃ 1000°N
°N = -11.11 (1-212 °f)
C °N = 2355.32 °N
or Approximately 2360 °N
Fp 0° °N

By interpolation:

100−0 1000 − 100


=
°c−0 °N−100°N

100 900 °c
=
°c −100°N

−1000 900 °c
=
900 900

n= -11.11 °c

2. Steam at a pressure of 150 psia and a temperature of 400°F occupies a volume


of 3.223 ft³/lb . Convert the temperature into "⁰R. ⁰K and ⁰C.

SOLUTION:
5
°C = ( F- 32 ) °R = F + 460
9
5
= ( 400 – 32 ) = 400 + 460
9

= 204.44 °C = 860 °R
°K = c + 273
= 204.44 °C + 273
= 477.44 °K

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