Heat Heat Capacity Heat capacity connects heat flow to temperature change: What is heat? Q = CΔT Heat (Q) is the “flow” or “transfer” of energy from Heat capacity C depends on material, and also on the quantity of one system to another material present. Eliminate quantity dependence by introducing Often referred to as “heat flow” or “heat transfer” specific heat c and molar heat capacity c′: Requires that one system must be at a higher Q = mcΔT Q = nc′ΔT m = mass n = number of moles temperature than the other Heat will only flow from the system with the higher Latent Heat temperature to the system with the lower temperature A phase change occurs when a solid melts to a liquid, a liquid boils to Heat will only flow from the system with the higher average a gas, a gas condenses to a liquid, and a liquid freezes to a solid. internal energy to the system with the lower average Each of these phase changes requires a certain amount of heat, internal energy although the temperature does not change. If a solid becomes liquid, or vice versa, the amount of heat per gram is Total internal energy does not matter. the latent heat of fusion. If a liquid becomes gas, or vice versa, the amount of heat per gram is the latent heat of vaporization A glass is filled with 100 g of ice at 0.00°C and 200 g of water at 25.0°C. Latent Heat (a) Characterize the content of the glass after equilibrium has been reached. Neglect heat transfer to and from the environment. (b) Repeat your calculations for 50.0 g of ice and 250 g of water. 1 Work Work Done by Thermal Systems Work can be done by thermal systems, as in the expansion of a gas. Using the definitions of work and pressure: V W = 2 PdV ∫V1 Note, work can be done on a thermal system, as in the compression of a gas. First Law of Thermodynamics Types of Transformations When temperature changes, internal energy has changed – Isobaric, ΔP = 0 may happen through heat transfer or through mechanical work W = PΔV First law is a statement of conservation of energy Work = Pressure*Change in Vol Change in internal energy of system equals the difference between the heat added to the system and the work done by the system Differential form Heat added +, heat lost -, work done by system +, work done on system – Isochoric, ΔV = 0 Internal Energy U is a state property W = 0 ⇒ΔU = Q Work W and heat Q are not But work and heat are involved in thermodynamic processes that change the state of the system 2 The PV diagram shows two states of a system containing 1.45 moles of an ideal gas (P1 = P2 = 450 Types of Transformations 2 3 3 N/m , V1 = 2.00 m , V2 = 8.00 m ). A) Draw an isobaric process from state 1 to state 2. Isothermal, ΔT = 0 B) Draw a two-step process that depicts and isothermal expansion from state 1 to V2 followed by an isochoric ΔU = 0, ⇒ W = Q increase in temperature to state 2. C) In both cases, calculate the work done, the heat added or lost, and the change in internal energy. Adiabatic, Q = 0 ⇒ΔU = -W Molar Specific Heats for Gasses Equipartition of Energy Molar specific heats for gasses are different if heat is added at constant pressure vs constant volume QP = nCPΔT QV = nCVΔT If the two processes result Isobaric, ΔP = 0 in the same temperature change, ΔU is the same. Diatomic, triatomic, etc. molecules are more complex Molecules can translate, rotate, and vibrate Isochoric, ΔV = 0 Energy is shared equally between the various degrees of freedom 3 o A certain gas has a specific heat cV = 0.0356 kcal/kg- C, which changes little over a wide temperature range. What is the atomic mass of the gas? What gas is it? Adiabatic, Q = 0 Assume an adiabatic and quasistatic expansion of an ideal gas. After a lot of calculus and algebra (see p 592): For the same increase in volume, an adiabatic process will result in a lower pressure and lower temperature than an isothermal process. What about work? Heat Transfer Conduction Conduction Time rate of heat transfer depends on Results from molecular interactions The material Specifically k = thermal conductivity Collisions? Area Energy is transferred through interaction Temperature difference Convection Thickness or length Results from the mass transfer of material Think fluid flow Radiation Differential form R-Value, Thermal Resistance Value Energy transferred by electromagnetic radiation (waves) Does not require a “medium” 4 Your refrigerator can be thought of as a box with six sides of total area 2.5 m2. The effective R value of the walls is 1.5 m2–K/W. The temperature inside is 5.0°C, Radiation while the temperature outside is 25°C. Calculate the rate of heat loss. Time rate of heat transfer depends on The material Specifically e = emissivity Area Surface area Temperature difference Experimentally determined to be proportional to the 4th power of T An experimentally determined Stefan-Blotzmann constant σ A surface that is “white hot” emits about 10 times more power than a “red hot” surface. What does this tell us quantitatively about the relative temperature? Blackbody Radiation Objects that become sufficiently hot will glow visibly; as they get hotter they go from red, to yellow, to a bluish white. This is electromagnetic radiation; objects at any temperature will emit it at various frequencies, from radio waves all the way to gamma rays. This radiation from a body in thermal equilibrium is called blackbody radiation, as it is purely thermal and doesn’t depend on any properties of the body other than its temperature and area. Deriving the energy density as a function of frequency and temperature required introducing some new concepts: Here, c is the speed of light: And h is Planck’s constant: 5.