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Unit 3 Temperature, Heat, and the First Law of Thermodynamics

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Absorption of Heat You heat an object It gets hot Heat Capacity (cal/K, or J/K) (add heat to it)(temperature increases) Specific Heat (cal/g · K, or J/kg·K)

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water By definition of heat, the specific heat of water is cal/g · K c = 1 cal/g · K higher than most other substance

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Latent Heat During some phase transitions (i.e. ice - water), heating does not lead to increase of temperature until the transition is completed Latent Heat (cal/g, or J/kg) The thermal energy required for the transition:

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Work Done During Volume Change Consider a gas cylinder of piston area A, gas pressure p, and gas volume V The gas expands, the piston moves by ds, and the volume changes from V to V+dV=V+A·ds The work done BY the gas: dW=F·ds=A·p·ds=p·dV The work done BY the gas during the volume change from V i to V f

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P-V Diagram is the area under the curve in the p-V diagram representing a path from V i to V f (Pay attention to the direction of the path!!) different areadifferent work Same V i and V f, different path Close cycle W = enclosed area

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The First Law of Thermodynamics For given initial and final points, Q - W is the same for all paths. The First Law of Thermodynamics: difference of internal energy heat added to the system work done by the system

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The First Law of Thermodynamics work done ON the system or Infinitesimal process internal energy The change of internal energy is path independent internal energy The internal energy is a state function

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n Adiabatic process: n Adiabatic process: Q = 0 ∆E int = -W n Cyclic process: n Cyclic process: ∆E int = 0 Q = W = Area enclosed by the cycle n Free expansion: n Free expansion: Q = 0, W = 0 ∆E int = 0 n Isovolumetric process: W = 0 ∆E int = Q

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Heat Transfer Mechanisms Heat Transfer Mechanisms n n Conduction – –through the materials n n Convection – –through the movement of a heated substance n n Radiation – –through emission of electromagnetic field

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Conduction Exchange of kinetic energy –Between molecules or atoms (insulators) –By “free electrons” (metals) Rate of heat transfer Temperature gradient Cross-section Thermal conductivity (W/m K)

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Convection n Natural convection Result from difference in density n Forced convection The heated substance is forced to move Heat transfer by the movement of a heated substance.

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Radiation Power of radiation Temperature Stefan-Boltzmann constant 5.67051 x 10 -8 W/m 2 K 4 Emissivity Area Radiation: Absorption: Net absorption:

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(a) The heat transferred to the water of mass m l is: Q w = c w m w ∆T + L V m s = (1 cal/gC˚)(220g)(100˚C-20.0˚C)+(539 cal/g)(5.00 g) = 20.3 kcal HRW 54E (5 th ed.). A 150 g copper bowl contains 220 g of water, both at 20.0˚C. A very hot 300 g copper cylinder is dropped into the water, causing the water to boil, with 5.00 g being converted to steam. The final temperature of the system is 100˚C. (a) How much heat was transferred to the water? (b) How much to the bowl? (c) What was the original temperature of the cylinder?

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(b) The heat transferred to the bowl is: Q b = c b m b ∆T = (0.0923 cal/gC˚)(150g)(100˚C-20.0˚C)= 1.11 kcal (c) Let it be T i, then -Q w - Q b = c c m c (T f -T i ) HRW 54E (5 th ed.). A 150 g copper bowl contains 220 g of water, both at 20.0˚C. A very hot 300 g copper cylinder is dropped into the water, causing the water to boil, with 5.00 g being converted to steam. The final temperature of the system is 100˚C. (a) How much heat was transferred to the water? (b) How much to the bowl? (c) What was the original temperature of the cylinder?

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Since the process is a complete cycle (beginning and ending in the same thermodynamic state), ∆E int = 0 and Q = W, Q CA = W- Q AB - Q BC = 15.0 J - 20.0 J - 0 = -5.0 J 5.0 J of energy leaves the gas in the form of heat. Q AB + Q BC + Q CA = W HRW 75E (5 th ed.). Gas within a chamber passes through the cycle shown in Fig. 19-37. Determine the net heat added to the system during process CA if the heat Q AB added during process AB is 20.0 J, no heat is transferred during process BC, and the net work dome during the cycle is 15.0 J.

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(b) The rate at which the ice melts is (a) The rate at which the heat is conducted along the rod HRW 84E (5 th ed.). A cylindrical copper rod of length 1.2 m and cross-sectional area 4.8 cm 2 is insulated to prevent heat loss through its surface. The ends are maintained at a temperature difference of 100˚C by having one end in a water-ice mixture and the other in boiling water and steam. (a) Find the rate at which heat is conducted along the rod. (b) Find the rate at which ice melts at the cold end.

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