temperature as given by what is commonly called the

ideal gas law. The ideal gas law is given by

PVmRT

where

Pabsolute pressure of the gas, Pa

Vvolume of the gas, m

3

mmass, kg

Rgas constant

Tabsolute temperature, Kelvin

What is the appropriate unit for R, if the above equa-

tion is to be homogeneous in units?

6.32. The amount of radiant energy emitted by a surface is

given by the equation whereqrepresents

the rate of thermal energy, per unit time, emitted by the

surface in watts;eis the emissivity of the surface 0 e

1 and is unitless;sis the Stefan-Boltzman constant

(s5.67 10

 8

);Arepresents the area of the surface

in m

2

;andTSis the surface temperature of the object

expressed in Kelvin. What is the appropriate unit fors,

if the above equation is to be homogeneous in units?

6.33. A person’s body temperature is controlled by (1) convec-

tive and radiative heat transfer to the surroundings,

(2) sweating, (3) respiration by breathing surrounding air

and exhaling it at approximately body temperature,

(4) blood circulation near the surface of the skin, and

(5) metabolic rate. Metabolic rate determines the rate of

conversion of chemical to thermal energy within a per-

son’s body. The metabolic rate depends on the person’s

activity level. A unit commonly used to express the meta-

bolic rate for an average person under sedentary condi-

tions, per unit surface area, is called met; 1 met is equal to

58.2 W/m

2

. Convert this value to Btu /hft
2
. Also,
calculate the amount of energy dissipated by an average
adult person sleeping for 8 hours, if he or she generates
0.7 mets and has a body surface area of 19.6 ft
2
. Express
your results in Btu and Joules (1 Btu 1055 Joules).
6.34. Thecalorieis defined as the amount of heat required to
raise the temperature of 1 gram of water by 1°C. Also, the
energy content of food is typically expressed inCalories
which is equal to 1000 calories. Convert the results of
the previous problem to Calories (1 Btu252 calories).
6.35. Convert the strength of selected materials given in
the accompanying table from MPa to ksi, where
1000 lbf/in
2
1 ksi.

qesAT

4

S ,

6.36. The density of water is 1000 kg /m

3

. Express the density
of water in lbm/ft
3
and lbm/gallon (7.48 gallons 1 ft
3
).
6.37. A unit that is generally used to express the insulating
value of clothing is called clo. 1 clo is equal to
0.155 m
2
°C / W. Express this value in U.S. Custom-
ary units (°Fft
2
h / Btu).
6.38. Start with 1 lbfft /s and convert it to Nm/s and show
that 1 lbfft /s is equal to 1.36 watts. Knowing that
550 lbfft /s is equal to 1 horsepower, how many
kilowatts is that?
6.39. Viscosity of fluid plays a significant role in the analyses
of many fluid dynamics problems. The viscosity of
water can be determined from the following correlation:

where

mviscosity (N/sm

2

)

Ttemperature (K)

c 1 2.414  10

 5

c 2 247.8 (K)

c 3 140 (K)

What is the appropriate unit for c 1 , if the above equa-

tion is to be homogeneous in units?

6.40. For the ideal gas law given in Problem 6.31, if the units

of P, V, m, and Tare expressed in lbf/ft

2

, ft

3

, lbm, and

a

c 2

Tc 3

mc 110 b

Problems 157

Ultimate Ultimate

strength strength

Material (MPa) (ksi)

Aluminum alloys 100 –550

Concrete (compression) 10 –70

Steel

Machine 550 – 860

Spring 700 –1,900

Stainless 400 –1,000

Tool 900

Structural Steel 340 – 830

Titanium alloys 900 –1,200

Wood (Bending)

Douglas fir 50 – 80

Oak 50 –100

Southern pine 50 –100

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