W12≠W12 II Volume Work depends on the path Work is area under curve of P(v) a)Work is path dependent; b) Properties only depend on states: c) Work is not a property, not a state variable d) when we say W1-2, the work between states I and 2, we need to specify the path e)For irreversible(non-reversible)processes, we cannot use PdV; either the work must be given or it must be found by another method Muddy points How do we know when work is done?(MP 0.3 10) Heat Heat is energy transferred due to temperature differences a) Heat transfer can alter system states b)Bodies dont"contain"heat; heat is identified as it comes across system boundaries c) The amount of heat needed to go from one state to another is path dependent d) Heat and work are different modes of energy transfer ferred e) Adiabatic processes are ones in which no heat is transfer I1) First Law of Thermodynamics For a system AE=Q-w E is the energy of the system Q is the heat input to the system, and w is the work done by the system E=U(thermal energy)+ Ekinetic Potential+ If changes in kinetic and potential energy are not important a)U arises from molecular motion b)U is a function of state, and thus au is a function of state(as is 4E c)Q and w are not functions Comparing(b)and(c) we have the striking result that d )40 is independent of path even though Q and w are not! 0-5
0-5 P Volume Work is area under curve of P(V) V1 V2 W1-2 ≠ P Work depends on the path V I I II W1-2 II a) Work is path dependent; b) Properties only depend on states; c) Work is not a property, not a state variable; d) When we say W1-2, the work between states 1 and 2, we need to specify the path; e) For irreversible (non-reversible) processes, we cannot use ∫PdV; either the work must be given or it must be found by another method. Muddy points How do we know when work is done? (MP 0.3) 10) Heat Heat is energy transferred due to temperature differences. a) Heat transfer can alter system states; b) Bodies don't "contain" heat; heat is identified as it comes across system boundaries; c) The amount of heat needed to go from one state to another is path dependent; d) Heat and work are different modes of energy transfer; e) Adiabatic processes are ones in which no heat is transferred. 11) First Law of Thermodynamics For a system, ∆E QW = − E is the energy of the system, Q is the heat input to the system, and W is the work done by the system. E = U (thermal energy) + Ekinetic + Epotential + .... If changes in kinetic and potential energy are not important, ∆U = Q −W . a) U arises from molecular motion. b) U is a function of state, and thus ∆U is a function of state (as is ∆E). c) Q and W are not functions of state. Comparing (b) and (c) we have the striking result that: d) ∆U is independent of path even though Q and W are not!
Muddy points What are the conventions for work and heat in the first law?(MP 0.4) When does E->U?(MP 0.5 12) Enthalpy: A useful thermodynamic property, especially for flow processes, is the enthalpy. Enthal s usually denoted by h, or h for enthalpy per unit mass, and is defined by H=U+PV In terms of the specific quantities, the enthalpy per unit mass is h=u+ Pv=u+P/p 13)Specific heats -relation between temperature change and heat input For a change in state between two temperatures, the"specific heat" is: Specific heat =@/(Tfinal- Tinitial) We must, however, specify the process, i. e, the path, for the heat transfer. Two useful processes are constant pressure and constant volume. The specific heat at constant pressure is denoted as Cp and that at constant volume as Cv, or cp and cyper unit mass and c For an ideal gas dh= cpdr and du=Cudr. The ratio of specific heats, Cp/cv is denoted by y This ratio is 1. 4 for air at room conditions The specific heats Cv and cp have a basic definition as derivatives of the energy and enthalpy Suppose we view the internal energy per unit mass, L, as being fixed by specification of T, the temperature and v, the specific volume, 1. e, the volume per unit mass.( For a simple compressible substance, these two variables specify the state of the system. Thus u=u(T, v) The difference in energy between any two states separated by small temperature and specific volume differences dt and dv is du The derivative(Ou/), represents the slope of a line of constant v on a u-T plane. The derivative is also a function of state, 1. e, a thermodynamic property, and is called the specific heat at constant volume, Cy. The name specific heat is perhaps unfortunate in that only for special circumstances is the derivative related to energy transfer as heat. If a process is carried out slowly at constant volume, n work will be done and any energy increase will be due only to energy transfer as heat. For such a 0-6
0-6 Muddy points What are the conventions for work and heat in the first law? (MP 0.4) When does E->U? (MP 0.5) 12) Enthalpy: A useful thermodynamic property, especially for flow processes, is the enthalpy. Enthalpy is usually denoted by H, or h for enthalpy per unit mass, and is defined by: H = U + PV. In terms of the specific quantities, the enthalpy per unit mass is h = u + Pv = u P + /ρ. 13) Specific heats - relation between temperature change and heat input For a change in state between two temperatures, the “specific heat” is: Specific heat = Q/(Tfinal - Tinitial) We must, however, specify the process, i.e., the path, for the heat transfer. Two useful processes are constant pressure and constant volume. The specific heat at constant pressure is denoted as Cp and that at constant volume as Cv, or cp and cv per unit mass. c h T c u T p p v v = = ∂ ∂ ∂ ∂ and For an ideal gas dh = cpdT and du = cvdT. The ratio of specific heats, cp/cv is denoted by γ. This ratio is 1.4 for air at room conditions. The specific heats cv. and cp have a basic definition as derivatives of the energy and enthalpy. Suppose we view the internal energy per unit mass, u, as being fixed by specification of T, the temperature and v, the specific volume, i.e., the volume per unit mass. (For a simple compressible substance, these two variables specify the state of the system.) Thus, u = u(T,v). The difference in energy between any two states separated by small temperature and specific volume differences, dT and dv is du = ∂u ∂T v dT + ∂u ∂v T dv The derivative ∂u ∂T v represents the slope of a line of constant v on a u-T plane. The derivative is also a function of state, i. e., a thermodynamic property, and is called the specific heat at constant volume, cv. The name specific heat is perhaps unfortunate in that only for special circumstances is the derivative related to energy transfer as heat. If a process is carried out slowly at constant volume, no work will be done and any energy increase will be due only to energy transfer as heat. For such a