حرارة وديناميكا حرارية المحاضرة الخامسة د/ محرز لولو

Heat and the first law of thermodynamics Chapter 2 Heat and the first law of thermodynamics

The aim of this chapter To describe the types of thermodynamics systems (isolated, open, and closed) To explain the thermodynamic process (isothermal, isobar, adiabatic and isochoric) Define the heat capacity, specific heat capacity, and latent heat). To define the heat, work, and energy. To apply the first law of thermodynamics To derive the relationship between the two heat capacities (Cp and Cv).

Natural systems tend toward states of minimum energy Thermodynamics A system: Some portion of the universe that you wish to study The surroundings: The adjacent part of the universe outside the system. The boundaries: The system should have boundaries separated it from the surroundings boundary A system A system surroundings a system: Some portion of the universe that you wish to study a glass of water plagioclase the mantle Changes in a system are associated with the transfer of energy lift an object: stored chemical  potential drop an object: potential  kinetic pump up a bicycle tire: chemical  mechanical  heat (friction + compression) add an acid to a base: chemical  heat The possible exchanges of heat, work or matter between the system and surroundings take place across this boundaries Natural systems tend toward states of minimum energy

Thermodynamic variables U- the internal energy all the potential and kinetic energy of the system. It is a state function depends only on the thermodynamic state of the system (P, V and T for a simple system) Q-the amount of heat added to the system (+) ve if the system gains heat from its surrounding (endothermic process) (-) ve if the system lose heat (exothermic process) W-the work done (+) ve if the work done by the system (-) ve if the work done on the system

1) Mechanical exchange (Expansion work) A system can exchange energy with its surroundings through two mechanisms: 1) Mechanical exchange (Expansion work) performing work on the surroundings 2) Thermal exchange (Heat transfer) transferring heat across the boundary

* A system is in thermodynamic equilibrium if it is in mechanical and thermal equilibrium. Mechanical equilibrium: the pressure difference between the system and its surroundings is infinitesimal; Thermal equilibrium: the temperature difference between the system and its surroundings is infinitesimal.

TWO WAYS TO INCREASE THE INTERNAL ENERGY, U. WORK DONE ON A GAS (Positive) HEAT PUT INTO A SYSTEM (Positive)

TWO WAYS TO DECREASE THE INTERNAL ENERGY, U. Wout hot HEAT LEAVES A SYSTEM Q is negative Qout hot -U Decrease WORK DONE BY EXPANDING GAS: W is positive

Types of thermodynamics systems Isolated system: matter and energy may not cross the boundary Adiabatic system: heat may not cross the boundary (constant amount of heat Q= const) Closed system: matter may not cross the boundary Open system: heat, work, and matter may cross the boundary.

Units of heat A calorie: is the energy required to raise the temperature of one gram of water form 14.5 to 15.5 ˚C 1cal=4.186 J 1 food calorie =1000 cal The BTU: is the energy required to raise the temperature of 1 lb of water form 63 to 64 ˚F Example 1: If you consume 2000 food calorie what is the energy gained in Joules

Joule experiment Joule found that, the loss in mechanical energy is proportional to the increase in temperature the constant of proportionality is equal 4.186 1cal=4.186 J DT M F Dx H2O W = FDx

Intensive and extensive property a. Intensive property: does not depend on the mass (m) or does not change with size of the system, denoted by lowercase letters, e.g., z. (like P and T) b. Extensive property: does depend on the mass (m) or does change with subdivision of the system, denoted by uppercase letters, e.g., Z. (like mass, volume, energy) An intensive property is also called a specific property if For example, volume V is an extensive property, so v=V/m (i.e., volume per unit mass) is a specific property and an intensive property.

Homogeneous vs heterogeneous a. A system is considered to be homogeneous if every intensive property has the same value for every point of the system. b. A system is said to be heterogeneous if the intensive property of one portion is different from the property of another portion.

Work Work = Force ´ Distance DW = F Dx The unit for work is the Newton-meter which is also called a Joule.

The mechanical work The mechanical work is defined as the amount of energy transfer to the system through external macroscopic force Dx P F A DV P = const

Remember the Zero law of thermodynamics

The first law of thermodynamic The first law states that the energy can neither be destroyed or created only transferred to other form. The mathematical form of the first law: The change in internal energy of a system is equal to the heat added to the system minus the work done by the system ΔU = Q-W

First Law of Thermodynamics Internal Energy ΔU = Q - W (Conservation of Energy) Heat Energy Work Done

THERMODYNAMIC STATE The STATE of a thermodynamic system is determined by four factors: Absolute Pressure P in Pascals Temperature T in Kelvins Volume V in cubic meters Number of moles, n, of working gas

THERMODYNAMIC PROCESS Increase in Internal Energy, U. Wout Initial State: P1 V1 T1 n1 Final State: P2 V2 T2 n2 Heat input Qin Work by gas

The Reverse Process Decrease in Internal Energy, U. Win Qout Work on gas Loss of heat Qout Win Initial State: P1 V1 T1 n1 Final State: P2 V2 T2 n2

Thermodynamic Processes A thermodynamic process is represented by a change in one or more of the thermodynamic variables describing the system. Each point on the curve represents an equilibrium state of the system. Our equation of state, the ideal gas law (PV = nRT), only describes the system when it is in a state of thermal equilibrium. MFMcGraw Chap15d-Thermo-Revised 5/5/10

Thermodynamic process * The transformation of a system between two states describes a path, which is called a thermodynamic process. * There are infinite paths to connect two states.

Thermodynamic process Isobaric – constant pressure (P=C) Isothermal –constant temperature (T=C) Isochoric – constant volume (V=C) Adiabatic – no heat transferred (Q=0)

The amount of heat is given by Q = nCPDT Isobaric Process An isobaric process is a constant pressure process. ΔU, W, and Q are generally non-zero Calculating the work done by an ideal gas is straightforward(see next slid) For ideal gas PV=nRT, P=const From Charl’s law The amount of heat is given by Q = nCPDT

The work done for the isobaric process The area under a PV curve gives the magnitude of the work done on a system. W< 0 for compression (V2 < V1) and W > 0 for expansion (V2 > V1). DW=PDV

Isobaric Process

Isothermal Process An isothermal process is a constant temperature process. Any heat flow into or out of the system must be slow enough to maintain thermal equilibrium. For ideal gases, if ΔT is zero, ΔU = 0 Therefore, Q = W Any energy entering the system (Q) must leave as work (W) For an ideal gas: PV= nRT= const →P1V1=P2V2

Chap15d-Thermo-Revised 5/5/10 An isothermal process implies that both P and V of the gas change (PVT). MFMcGraw Chap15d-Thermo-Revised 5/5/10

Chap15d-Thermo-Revised 5/5/10 Isothermal Process An isothermal process implies that both P and V of the gas change (PVT). Chap15d-Thermo-Revised 5/5/10

The work done in the isothermal process For an ideal gas PV=nRT

Isochoric (Isometric) Process An isochoric process is a constant volume process. When the volume of a system doesn’t change DV = 0, it will do no work on its surroundings. W =PDV = 0 ΔU = Q= nCvDT Heating gas in a closed container is an isochoric process

Isochoric process For an ideal gas PV=nRT

Isometric Process

Adiabatic Process An adiabatic process transfers no heat therefore Q = 0 ΔU = Q-W → W=-ΔU When a system expands adiabatically, W is positive (the system does work) so ΔU is negative. When a system compresses adiabatically, W is negative (work is done on the system) so ΔU is positive.

Adiabatic Process

The adiabatic process The frst law of thermodynamics for an adiabatic process can be stated as: dQ = nCV dT + PdV = 0 ……………………..(1) where CV is the molar specfic heat at constant volume. If we write the Ideal Gas law as: PdV + VdP = nRdT then: …………………..(2) and substitute Eq (2) into Eq (1), we obtain

But CP= CV+R where CP is the molar specific heat at constant pressure. CPPdV + CVV dP=0 By dividing by CVPV

To go from the state (Vi, Pi) by the path (a) to the state (Vf, Pf) requires a different amount of work then by path (b). To return to the initial point (1) requires the work to be nonzero. The work done on a system depends on the path taken in the PV diagram. The work done on a system during a closed cycle can be nonzero.

Reversible and irreversible thermodynamic Process The process is said to be an irreversible process if it cannot return the system and the surroundings to their original conditions . MFMcGraw Chap15d-Thermo-Revised 5/5/10

Summary of Thermodynamic Processes MFMcGraw Chap15d-Thermo-Revised 5/5/10