Question

Determine the fundamental dimensions of the following quantities.

a. Fuel comsumption with units of kg/Wh

b. Latent heat with units of J/kg

c. Specific weight with units of N/m³

d. Molar heat capacity with units of J/molK

e. Rate of drying with units of kg/m²h

f. Thermal resistance with units of Km²/W

A= Ampere = Unit of current

J = Joule = Unit of energy

K = Kelvin = Unit of temperature

N = Newton = Unit of force

V = Volt = Unit of voltage

W = Watt = Unit of power

Answer 1

Part a

Fuel comsumption with units of kg/Wh

Watt = W = J/s = N-m/s = (kg-m/s2)-m/s = kg-m2/s3

hour = h = 3600 s

We will not use number so leave the number

Fuel comsumption with Fundamental units

kg/Wh = kg / ( kg-m2-s/s3) = s2/m2

Part b

Latent heat with units of J/kg

J = N-m = (kg-m/s2)-m = kg-m2/s2

Latent heat with Fundamental units

J/kg = (kg-m2/s2) / kg = m2/s2

Part c

Specific weight with units of N/m3

N = (kg-m/s2)

Specific weight with Fundamental units

N/m3 = (kg-m/s2) / m3 = kg/(s2-m2)

Part d

Molar heat capacity with units of J/molK

J = N-m = (kg-m/s2)-m = kg-m2/s2

mol can be converted into kilograms (kg) by multiplying by molecular weight.

Molar heat capacity with Fundamental units

J/mol·K = (kg-m2/s2) / (kg-K) = m2/(s2-K)

Part e

Rate of drying with units of kg/m2h

Rate of drying with Fundamental units

kg/m2h = kg/m2-s

Part f

Thermal resistance with units of Km2/W

Km2 = 1000 m2

Watt = W = J/s = N-m/s = (kg-m/s2)-m/s = kg-m2/s3

Thermal resistance with Fundamental units

Km2/W = m2/(kg-m2/s3) = s3/kg

Fundamental units

Kg = kilogram = unit of mass

m = meter = unit of length/distance

s = seconds = unit of time

K = Kelvin = Unit of temperature