HEAT FLOW & THE FIRST LAW HEAT is the FLOW of ENERGY because of a temperature difference. The units...

HEAT FLOW & THE FIRST LAW

HEAT is the FLOW of ENERGY because of a temperature difference.

The units of HEAT are Joules/s or BTU/s or Calories/s BTU (British Thermal Unit) =1055 J

=252.02 cal Calorie (c ) = 4.1855 J

Food calorie (C) = 1 kcal =1000 cal (c)


The Calorie is defined as the amount of heat added 1 gram of water between 14.5 and 15.5 oC to raise it 1oC.

A food calorie or kilocalorie is the amount of heat added to 1 kg of water (a liter) between 16.5 and 17.5 oC to raise it one degree Celsius.


The BTU is the amount of heat added to 1 lb of water (averaged over the temperature range of 32oF to 212oF) one degree Fahrenheit.

Both the BTU and calorie are non-metric units. The calorie will eventually be phased out in preference to the Joule.


The heat flow must be made so that thermal equilibrium occurs at each stage of the process and an equation of state may be used. These changes must be done slowly (compared to propagation of molecules, the speed of sound)

V = 330 m/s in air at STP.


The processes of heating must be reversible. (So the process can traverse the same path on a P-V diagram)

There are irreversible processes which are not controlled and the system is not in thermal equilibrium, so these are not considered. These are not considered.


In order to measure the heat flow through a substance one needs to know the HEAT CAPACITY C, so one writes:

dQ = C dT where dQ is the small heat flow and

dT is the small amount of temperature change.


For finite changes one writes: ΔQ = C ΔT One can define specific heat capacity c = ΔQ/mΔT

for a one gram mass of the substance.

Molar heat capacity c’ = ΔQ/nΔT for one mole of the substance.


Where C = m c = n c’ m = mass and n = number of molesC has units of cal/Kc has units of cal/(g K)c’ has units of cal/mol KAlso c’ = Mc where M is molecular wt (g) (See Table 18-1 for values.)


The heat capacity is C = C(V,T) So C depends on how P,V,and T

change dQ = Cv dT (isochoric) dQ = Cp dT (isobaric) (later we’ll see that Cp ≥ Cv ) The measurement of heat capacities is

Adiabatic Calorimetry.


Heat can also occur during phase changes because changes in molecular form either release or absorb energy. This occurs during melting or freezing or boiling or condensation or during sublimation or deposition. During these processes, the temperature does not change so they are called Latent heats.


The Latent Heats are measured in three different units kJ/mol, kJ/kg, cal/g

Your text has a table of Latent Heats, Melting and Boiling Points (18-2)

Latent heats depend on p and T. Latent heat fusion heat

vaporization (H2O) 79.7 cal/g 540 cal/g (1 atm) 333.5 kJ/kg 2257 kJ/kg (1 atm)

First Law of Thermodynamics Applied to the Human Body

Food enters the body containing chemical energy Some is converted to stored chemical energy and some

to thermal energy Then chemical energy is converted to work (mechanical

energy) and some heat is released Sometimes the body has to do work to replace heat lost

(shivering) If the internal energy of the body is constant then food

energy must equal heat loss and work done What happens if not?

FoodChemical Energy Work

HeatThermal Energy

Results of U

Changes in the internal energy result in changes in the measurable macroscopic variables of the system Pressure Temperature Volume

For the human body it is usually temperature or volume (isobaric)

Metabolic Rates (Cal/m2-hr)

Sleeping 35Lying awake 40Sitting 50Standing 60Walking 140Running 600Shivering 250

Your surface area can beapproximated using theformula SA = .202m.425 x h.725

where m is in kg and h is inmeters. Calculateyour surface area

The metabolic rate at rest is the basal metabolic rate. The surface area of a 70 kg man of height 1.55m is about 1.70 m2. His metabolic rate is therefore 40 x 1.70 = 68 Cal/hr while lying awake.

Heat and Life We need energy to function (blood circulation,

cell repair, etc.) Even at rest a 70 kg person consumes about 70

Cal/hr The energy needed depends on a persons weight

and build However, it has been found that human energy

consumption (usage) divided by a person’s surface area is approximately the same for most people

It is given a unit of Cal/m2-hr and called metabolic rate

Measuring Metabolic Rate

The metabolic rate is related to oxygen consumption by

About 80 W is the basal metabolic rate, just to maintain and run different body organs

24.8 oVUt t

Various Metabolic Rates

Aerobic Fitness One way to measure a person’s

physical fitness is their maximum capacity to use or consume oxygen

Energy Output vs. Food Intake Food requirements depend on activity levels Consider this schedule:Activity Energy (Cal/m2) For a person of SA 1.7m2

this is 2320(1.70)8 hr of sleep 280 or 3940 Cal per day.8 hr of moderate activity 1200 This could be met by a 4 hr of reading 240 diet of:1 hr of heavy exercise 300 400g of carbs 1600 Cal3 hr of dressing, eating 300 200g of Protein 800 CalTotal 2320 171g of fat 1540 Cal

3940 Cal

Weight Gain vs. Weight Loss They are stored as tissue (fat or muscle) Lack of caloric intake results in the body getting

energy from stored fat first (9 Cal/g) and then proteins (4 Cal/g)

The average person can go 50 days without food Angus Barbieri of Scotland consumed only tea, coffee

and water from June 1965 to July 1966 reducing his body weight from 472 lbs to 178 lbs

Pregnant women need an extra 136 Cal/day which can come from an increased appetite or a decrease in physical activity

The body cannot eliminate excess calories

Efficiency of the Human Body

Efficiency is the ratio of the mechanical power supplied to the metabolic rate or total power input

Example Hiking Howard’s Knob

Suppose one starts out from King Street and climbs Howard’s Knob. How much

energy is needed? Δh=1400 ft=427 m Assume m=80 kg PE= mgh = 80 kg 9.8 (m/s2) 427 m = 335 kJ/4.186kj/kcal = 80 kcal ε=.2ΔPE(ME)= εΔPEfood ΔPEfood =400 kcal

HEAT FLOW IN MATERIALS

Heating occurs by Radiation, Convection and Conduction. In materials it is by conduction.

ΔQ/Δt = κ A ΔT/L where is κ is the thermal

conductivity. The unit of conductivity w/(mK) ,see

text Table 18-3 for κ values.


Materials which have poor thermal conductivity can be thought of as thermal resistors. R = L/κ

the metric unit of R is m2 K /W in the English System R is ft2 oF

hr/BTU R(value)=1 ft2 oF hr/BTU= 0.18 m2 K/W R value of 4 inch fiberglass =11


R value for 6 inch fiberglass is =19 R value for 3/8 plasterboard is =0.32 R value for glass is = 0.02 R value for plywood = 0.6 R value for brick is between 0.6 1.0 If A = 1 ft2 , ΔT =(68-18) =50 oF, R=11 then, Q/t = 4.6 BTU/hr = 1.35 W.


In analogy with electrical phenomena one can apply the mathematical

formalism of electrical phenomena to similar thermal phenomena.

Electrical Thermal R R/A R in series R1 /A + R2 /A =RT /A


Electrical Thermal R in parallel A1 /R1+ A2 /R2 = AT /Reff

Conductivity σ κρ (resistivity) = 1/σ 1/κ Δ V Δ T i = ΔQCharge /Δt ΔQHeat/Δt

Flux i = Δ V/R ΔQHeat/Δt = ΔT A/R


Let Electrical Conductivity σ = 1/ρ The ratio of the thermal conductivity

and the electrical conductivity and the Kelvin Temperature is the

Widermann- Franz –LorentzRatio σ/κT = 3 (R/F)2 = 2.23 x 10-8 (V/K)2 Approximately constant for metals.

Work in a THERMAL SYSTEM

Consider a piston of area A being pushed outward by a gas in a volume V

The WORK DONE by the gas is: dW = F dx = p A dx = p dV

W = V1∫V2 p dV

Sign of work determined by V1 > or < V2

HEAT FLOW & THE FIRST LAW HEAT is the FLOW of ENERGY because of a temperature difference. The units...

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