Dr. Johnny B. Holmes

Introduction
Fluids
Temperature and Heat
Laws of Thermodynamics
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In this fourth part of the course we consider the ideas of pressure, temperature, and heat.

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Outline
Supplementary Homework Problems
Answers to Problems
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Outline

1. Pressure
1. definition: P_ressure = F/A
2. gauge pressure = P_absolute - P_atm
3. units: N/m², lbs/in²., atmospheres, mm of mercury, inches of mercury, bars
4. hydrostatics: P is same everywhere if ignore effects of gravity
2. Effect of gravity on fluid PP
1. density: r = m/V (units: kg/m³)
2. specific gravity: s.g. = r _object/r _water (units: none)
3. effect of height of column of fluid: P(h) - P_o = rgh
4. the manometer
1. basic instrument (760 mm of Hg = 1 atm = 1.01 x 10⁵ Nt/m²)
2. blood pressure
3. Archemides' principle: buoyant force: F_buoy = r_fluidVg
3. Fluid flow (laminar, not turbulent) QQ
1. Eq. of continuity: (conservation of mass) A₁ v₁ = A₂ v₂ .
2. Bernoulli's equation: (conservation of energy)
   1/2rv₁² + rgh₁ + P₁ = 1/2rv₂² + rgh₂ + P₂ + P_lost

b) viscous force: F_vis = hAv/d,

3. flow through a pipe
1. velocity = v = DP(R²-r²)/(4hL)
2. fluid flow: Q = V_ol/t = (p R⁴DP)/(8hL)
3. resistance: R where Q = P/R, so R = (8hL)/(pR⁴)
4. Power = P Q [for the heart: Q = 83 ml/s = 8.3 x10^-5 m³/s, P = 100 mm of Hg, so Power = 1.1 Watt; compare to avg power of 100 Watts which corresponds to 2000 Calories/day]

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LETTER PROBLEMS:

PP. a) What is the gauge pressure at a depth of 10 ft under water? b) What is the absolute pressure at this depth?

QQ. A hose of inside diameter 1 cm and length 30 meters carries water from the faucet at a house out to the garden. Assume the garden and the house are at the same height. a) If the pressure at the garden side of the hose is atmospheric, and the pressure at the house side is 2 times atmospheric, and the flow of water through the pipes leading up to the faucet at the house causes negligible pressure decrease (i.e., only the flow through the hose causes pressure decrease), what is the volume flow of water per time through the hose? b) If the garden were located up a hill of vertical height 6 meters, what would the volume flow of water per time be?

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PP. a) 29,870 Nt/m²; b)130,870 Nt/m².

QQ. a) 8.25 x 10^-4 m³/sec = .825 liters/sec; b) .345 liters/sec.

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Outline
Supplementary Homework Problems
Answers to Problems
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Outline

1. Thermal effects and measuring temperature:
1. thermal expansion: DL = a L(DT); D V = b V(DT)
2. pressure and temperature: DP µ DT
3. electrical resistance and temperature: metals & semiconductors
2. Temperature scales
1. relative zero: °F and °C
2. absolute zero: R and K
3. Kinetic Theory of Gases RR
1. pressure and collisions of molecules [P = F/A = S Dp/(Dt A)]
2. temperature and kinetic energy of molecules [1/2mv² µ T]
3. ideal gas law: PV = NkT where kT = (2/3)KE = (1/3)mv² _(avg)
4. using R = N_Ak and n = N/N_A, PV = nRT (T must be absolute temp)
5. what is an "ideal" gas: negligible size, elastic collisions
4. Heat capacity (DE/DT) of ideal gas
1. at constant volume (no work lost): C_V = (3/2)nR for monatomic gas
2. at constant pressure (work = PV is lost): C_P = C_V + nR = (5/2)nR
3. for diatomic gas, add 2 rotation modes: C_V = (5/2)nR, C_P = (7/2)nR
5. Heat capacity of other materials
1. for triatomic gases, add 1 more rotation mode
2. for higher temperatures, activate vibration modes
3. for solids, need to consider possible vibrational modes - at high temperatures get 3nR
6. Latent heats
1. of vaporization
2. of fusion
7. Heat Transfer SS,TT,UU,VV,WW
1. conduction: Q/t = kA(DT)/L , or Q/t = A(DT)/R where R = S (L_i/k_i)
1. metric units of R: m² °C / Watt
2. hardware store units-British for R: ft² °F hr / B.T.U.
3. conversion: 1 ft² °F hr / BTU = 0.176 m² °C / Watt
2. convection: Q/t = (heat capacity) (air exchanges/time) (DT)
1. for air: molar heat capacity = (7/2)R
2. for air: amount in moles = n = PV/RT
3. radiation: Q/t = e s A(T_out⁴ -T_in⁴ )
4. evaporation: sweat and latent heat of water

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LETTER PROBLEMS:

RR. What properties determine that a gas is "ideal". How does the pressure of a real gas compare to that of an "ideal" gas under the same n, V, and T since a real gas cannot perfectly match the "ideal" gas. Explain your answer.

SS. A person sweats to cool off in hot weather. Assume that a person does work so that on average 120 Watts of power show up as heat that needs to be removed solely by the evaporation of sweat. Further, assume that the sweat starts out at a temperature of 100°F. It is elevated to boiling temperature and then is boiled away (evaporated). [Although this does not occur uniformly for all the sweat - you would get scalded! - it is a good approximation for individual molecules of water.] How much water will be lost this way over an 8-hour work period?

TT. How much energy is lost per second due to conduction if 6 inches of fiber glass insulation (R-value for 6" = 18.8 ft²*°F*hr/B.T.U.) is used in all ceilings and walls in a house that is 50 ft. long and 30 feet wide and all walls are 8 feet in height and the temperature inside is 72°F and the temperature outside is 0°F (neglect windows and floors) ? How much would it cost to keep the house at 72°F if this temperature held constant for 1 month and the cost of electricity is $.05/(Kw*hr) ?

UU. For the same situation as in problem TT above, how much energy is lost per second through 10 windows each of area 1 square meter and each window consists of only one sheet of flat glass of thickness 0.125 inches [ k = 2 x 10^-3 cal/(s*cm*°C) ]? How much would it cost to heat the house now including losses from the windows and walls?

VV. What is the R-value for the single pane windows of problem UU?

WW. For the house in problem UU, how much energy would it take to heat the house from 0°F to 72°F if you consider only the air in the house and not the furnishings or the walls? (Be careful to consider the expansion of the air. Treat air as an ideal diatomic gas of 75% N₂ and 25% O₂. Also assume that the pressure remains that of 1 atmosphere.) How much would this cost? Assuming 1 air change per hour with no heat exchange between the incoming cold air and the outgoing warm air, how much would it cost to overcome convective heat losses for the house?

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SS. 1.37 liters of water (1.37 kg).

TT. 3,122 Watts; $112.40/month.

UU. 105,474 Watts; $3,797.06 + $112.40 = $3,909.46 for one month.

VV. 0.021 ft²*°F*hr/B.T.U

WW. 17,470,000 Joules = 4.85 kW*hrs; $0.24 ; $174.72 per month.

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Outline
Supplementary Homework Problems
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Outline

1. First Law of Thermodynamics: conservation of energy
   DU = Q - W (U in internal energy, Q is heat added, W is work done)
2. Second Law of Thermodynamics XX
1. probability: system tends to go to its most probable state
2. entropy: measure of probability of the state; since systems tend to go to the most probable state, systems tend to have their entropy increase
3. heat engines and efficiency
1. Eff_iciency = (Work done) / (Heat added) = (Q_hot - Q_cold) / Q_hot
2. Most efficient is Carnot engine: Eff = (T_hot - T_cold) / T_hot

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LETTER PROBLEMS:

XX. (a) State the first law of thermodynamics and tell where it comes from. (b) State the second law of thermodynamics and tell where it comes from.

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