Physics Quiz: Units, Measurement, and Heat Transfer

Conversion of Units

• 1 watt = 1 joule/second
• 1 foot = 12 inches

Relationship between Centigrade and Fahrenheit

• 9°C = 5°F - 160

Heat Transfer by Conduction

• Fourier's law states that the rate of conduction is proportional to the area and temperature gradient in the direction of heat flow
• Fourier's equation: Q = kA(t1 - t2)/L
• Where Q = quantity of heat, A = area, k = coefficient of thermal conductivity, t1 - t2 = temperature difference, and L = thickness
• q = quantity of heat transferred in unit time, given by q = kA(t1 - t2)/L

Coefficient of Thermal Conductivity

• k is a characteristic constant for each material
• k is the heat passing in unit time from one face of a cube of unit side to the opposite face, when the temperature difference is kept at one unit
• Thermal conductivities vary considerably, ranging from high values in metals to low values in gases

Unit Conversions

• q = Joule/second (or) Watt, k = Wm-1 K-1, A = m2, t1-t2 = ºK, L = m
• Example: k = 17 Wm-1 K-1, A = 20 cm2 = 20 x 10-4 m2, t1-t2 = 10 ºK, L = 1 mm = 1 x 0.001 m, q = 340 Watt

Heat Loss through a Brick Wall

• Example: Find the heat loss per square foot of surface through a brick wall 18 inches thick, with an inner surface temperature of 250 ºF and an outer surface temperature of 100 ºF, and a thermal conductivity of 0.4 Btu hr-1 ft-1 ºF-1
• Solution: q = 40 Btu/hr

Conduction of Heat through a Compound Layer

• The temperature difference is the driving force for heat transfer, and the resistance is given by L/KA
• Example: Calculate the heat flow through a compound layer with thermal conductivities k1, k2, and k3, and thicknesses L1, L2, and L3

Thermal Conductivities of Materials

• Copper: 379 Wm-1 K-1
• Aluminum: 242 Wm-1 K-1
• Steel: 43 Wm-1 K-1
• Stainless steel: 17 Wm-1 K-1
• Borosilicate glass: 1 Wm-1 K-1
• Water: 0.6 Wm-1 K-1
• Diatomite: 0.07 Wm-1 K-1
• Glass wool: 0.06 Wm-1 K-1
• Air: 0.03 Wm-1 K-1

Example Problems

• Example 1: Calculate the amount of heat that will flow through a sheet of steel 10 mm in thickness, 0.6 m wide and 1 m long, in 30 minutes with a temperature of 70 ºC on one side and 30 ºC on the other
• Example 3: Find the heat loss per square foot of surface through a brick wall 18 inches thick, with an inner surface temperature of 250 ºF and an outer surface temperature of 100 ºF, and a thermal conductivity of 0.4 Btu hr-1 ft-1 ºF-1