Practice Problems for Section B.3

CinChE Units Conversion Primer

PB.3.1: Convert m' = 575 g to lbm PB.3.6: Convert n' = 220 g-mol to lb-mol

Current state units: g Current state units: g-mol Goal state units: lbm Goal state units: lb-mol Equivalence: 453.592 g ≡ 1 lbm Equivalence: 453.592 g-mol ≡ 1 lb-mol

1lb 1lb-mol CF ==> m CF ==> 453.592 g 453.592 g-mol

PB.3.2: Convert m' = 1000 lbm to kg PB.3.7: Convert n' = 523.5 g-mol to kg-mol

Current state units: lbm Current state units: g-mol Goal state units: kg Goal state units: kg-mol Equivalence: 2.20462 lbm ≡ 1 kg Equivalence: 1000 g-mol ≡ 1 kg-mol

1kg-mol 1kg CF ==> CF ==> 1000 g-mol 2.20462 lbm

PB.3.3: Convert L' = 6048 cm to ft PB.3.8: Convert P' = 33 atm to bar

Current state units: cm Current state units: atm Goal state units: ft Goal state units: bar Equivalence: 30.48 cm ≡ 1 ft Equivalence: 1 atm ≡ 1.01325 bar

1ft 1.01325 bar CF ==> CF ==> 30.48 cm 1atm

6 2 PB.3.4: Convert L' = 6096 m to ft PB.3.9: Convert P' = 6.06 x10 dyne/cm to atm

Current state units: m Current state units: dyne/cm2 Goal state units: ft Goal state units: atm Equivalence: 1 m ≡ 3.2808 ft Equivalence: 1.01325 x 106 dyne/cm2 ≡ 1 atm

3.2808 ft 1atm CF ==> CF ==> 1m 1.01325× 1062 dyne/cm

3 PB.3.5: Convert t' = 21.75 hr to min PB.3.10: Convert V' = 25 ft to gal

Current state units: hr Current state units: ft3 Goal state units: min Goal state units: gal Equivalence: 1 hr ≡ 60 min Equivalence: 1 ft3 ≡ 7.4805 gal

60 min 7.4805 gal CF ==> CF ==> 1hr 1ft3

Practice Problems for Section B.4

PB.3.1: Convert m' = 575 g to lbm PB.3.6: Convert n' = 220 g-mol to lb-mol

Current state units: g Current state units: g-mol Goal state units: lbm Goal state units: lb-mol Equivalence: 453.592 g ≡ 1 lbm Equivalence: 453.592 g-mol ≡ 1 lb-mol

1lb 1 lb-mol DE: m= 575 g m = 1.27 lb DE: n= 220 g-mol = 0.485 g-mol 453.592 g m 453.592 g-mol

PB.3.2: Convert m' = 1000 lbm to kg PB.3.7: Convert n' = 523.5 g-mol to kg-mol

Current state units: lbm Current state units: g-mol Goal state units: kg Goal state units: kg-mol Equivalence: 2.20462 lbm ≡ 1 kg Equivalence: 1000 g-mol ≡ 1 kg-mol

1kg 1 kg-mol DE: m= 1000 lb = 453.6 kg DE: n= 523.5 g-mol = 0.5235 kg-mol m 1000 g-mol 2.20462 lbm

PB.3.3: Convert L' = 6048 cm to ft PB.3.8: Convert P' = 33 atm to bar

Current state units: cm Current state units: atm Goal state units: ft Goal state units: bar Equivalence: 30.48 cm ≡ 1 ft Equivalence: 1 atm ≡ 1.01325 bar

1ft 1.01325 bar DE: L= 6048 cm = 198.4 ft DE: P= 33 atm = 33.44 bar 30.48 cm 1atm

6 2 PB.3.4: Convert L' = 6096 m to ft PB.3.9: Convert P' = 6.06 x10 dyne/cm to atm

Current state units: m Current state units: dyne/cm2 Goal state units: ft Goal state units: atm Equivalence: 1 m ≡ 3.2808 ft Equivalence: 1.01325 x 106 dyne/cm2 ≡ 1 atm

3.2808 ft 6 dyne 1 atm = = P= 6.06×= 10 5.981 atm DE: L 6096 m 20,000 ft DE: 2 cm 6 dyne 1m 1.01325× 10 2 cm

3 PB.3.5: Convert t' = 21.75 hr to min PB.3.10: Convert V' = 25 ft to gal

Current state units: hr Current state units: ft3 Goal state units: min Goal state units: gal Equivalence: 1 hr ≡ 60 min Equivalence: 1 ft3 ≡ 7.4805 gal

60 min 7.4805 gal DE: t= 21.75 hr = 1305 min DE: V= 25 ft3 = 187.01 gal 1hr 1ft3

Practice Problems for Section B.6

o o o PB.6.1: Convert ∆T' = 82 ∆ F to ∆ R PB.6.4: Convert ∆T' = 127 ∆K to ∆ R

Equivalence: 1 Δ°F ≡ 1 Δ°R Equivalence: 1 ΔK ≡ 1.8 Δ°R

1∆R 1.8 ∆R DE: ∆=T 82 ∆F = 82 ∆R DE: ∆=T 127 ∆K =228.6 ∆ R 1F∆ 1K∆

o o o PB.6.2: Convert ∆T' = 22 ∆ C to ∆ F PB.6.5: Convert ∆T' = 67 ∆ C to ∆K

Equivalence: 1 Δ°C ≡ 1.8 Δ°F Equivalence: 1 Δ°C ≡ 1 ΔK

1.8 ∆F 1∆K DE: ∆=T 22 ∆C = 39.6 ∆F DE: ∆=T 67 ∆ C =67 ∆K 1C∆ 1C∆

o o o PB.6.3: Convert ∆T' = 98.6 ∆ F to ∆ C PB.6.6: Convert ∆T' = 250 ∆ R to ∆K

Equivalence: 1 Δ°C ≡ 1.8 Δ°F Equivalence: 1 ΔK ≡ 1.8 Δ°R

1∆C 1∆K DE: ∆=T 98.6 ∆F = 54.78 ∆C DE: ∆=T 250 ∆ R =138.89 ∆K 1.8∆ F 1.8∆ R

The unit equivalences for delta degree are used to convert only three quantities—heat capacity (e.g., kJ/mol·°C), thermal conductivity (e.g., J/s·m·°C), and heat transfer coefficient (e.g., BTU/h·ft2·°F) in chemical engineering. A common practice is to express the delta degree without the delta in the units of these three quantities. You must remember this practice when working with these three quantities.

Practice Problems for Section B.7

o o o PB.7.1: Convert T' = 202 F to R PB.7.4: Convert T' = 535.65 K to C

DE: T= 202 F + 459.67= 661.67 R DE: T= 535.65 K - 273.15= 262.5 C

o o o o PB.7.2: Convert T' = -13 C to F PB.7.5: Convert T' = 223 C to F

9 9 DE: T=−=( 13 C) + 32 8.6 F DE: T= ( 223 C) + 32= 433.4 F 5 5

o o o o PB.7.3: Convert T' = 67 F to C PB.7.6: Convert T' = 18 F to C

5 5 DE: T=( 67 F −= 32) 19.44 C DE: T=( 18 F −=− 32) 7.78 C 9 9

Practice Problems for Section B.8

m m PB.8.1: Convert v' = 5280 miles to miles PB.8.2: Convert v' = 3.600 to h s s h

Equivalence: 1 h ≡ 3600 s Equivalence: 1 h ≡ 3600 s

miles 1h miles mm3600 s DE: v= 5280 = 1.47 DE: v= 3.600 = 12 960 hs3600 s sh1h

Practice Problems for Section B.9, Part 1 of 2

PB.9.1: Convert 10 000 dyne to lbf

0.22481 lb DE: F= 10 000 dyne f = 0.02248 lb 1× 105 dyne f

g lbm PB.9.2: Convert 0.7861 to cm3 ft3

g 1lb 30.4833 cm lb DE: ρ= 0.7861 m ⋅ = 49.07 m cm3 453.592 g 133 ft ft3

dyne PB.9.3: Convert 115 to N cm2 m2

dyne 1 N 10022 cm N DE: P= 115 ⋅ = 11.5 cm2 1× 105 dyne 1m22 m2

m cm PB.9.4: Convert 1800 to s2 h2

m 100 cm 360022 s cm DE: a= 1800 ⋅ =2.333 × 1012 sh2 1m 1h22 2

lb PB.9.5: Convert 32.56 g to m h s

g 1lb 1h lb DE: m = 32.56 m ⋅ =1.994 × 10−5 m hs453.592 g 3600 s

Practice Problems for Section B.9, Part 2 of 2

3 3 PB.9.6: Convert 35 m to ft

3.280833 ft DE: V= 35 m33 = 1236 ft 1m33

lbm kg PB.9.7: Convert 62.43 to ft3 m3

3 lbm 0.453592 kg 35.3145 ft kg DE: ρ= 62.43 3 ⋅ 33= 1000 ft 1lbm 1m m

lbf PB.9.8: Convert 44.1 to atm in2

lbf 1atm DE: P= 44.1 22 = 3.001 atm in 14.696 lbf /in

dyne PB.9.9: Convert 0.055 kPa to cm2

1.01325× 106 dyne/cm2 dyne DE: P= 0.055 kPa = 550 101.325 kPa cm2

PB.9.10: Convert 124 lbf to newton and kgf

1N DE: W= 124 lbf = 552 N 0.22481lbf

0.453592 kgf DE: W= 124 lbff = 56.25 kg 1lbf

Note that some force units equivalences are 1 lbf ≡ 0.453592 kgf ≡ 453.592 gf .

In Chapter 3 of this CinChE manual, you can find most units equivalences that you will need in Table “gotche”. You are to consult the website of www.onlineconversion.com for other units equivalences.