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Lecture 6: the first law and more non-flow processes The isobaric (constant pressure) process • consider a constant pressure process p dv
1
2
v
w = ∫ p dv = p (v 2 − v1 )
2 1
•
there is a small step dv in the process, thus dw = p dv for that small step, the NFEE dq − dw = du gives dq = du + p dv dw •
= du + p dv + v dp = du + d ( pv )
•
note: 1. adding v dp adds nothing because in a constant pressure process dp = 0 2. The last step cannot be taken if the change is finite because for finite changes ∆( pv) ≠ p∆v + v∆p . A little care with the mathematics is needed here. let us now define a new thermodynamic property, the enthalpy h, h = u + p v,
•
H = U + pV
• •
thus, in general,
dh = du + d ( p v )
the enthalpy h is clearly a property since it can be found from u, p and v, all of which are properties. and so, for this isobaric, non-flow process only, dq = dh further, if we integrate from state 1 to state 2, q = ∆h , Q = ∆ H
•
•
The specific heat at constant pressure • recall from the last lecture that the “the specific heat of a substance is the amount of energy required to raise the temperature of 1 kg of the substance by 1°C”.
•
this then led us to define the specific heat at constant volume, cv ⎛ ∂u ⎞ cv = ⎜ ⎟ ⎝ ∂T ⎠ v we can therefore also define the specific heat at constant pressure, ⎛ ∂h ⎞ cp = ⎜ ⎟ ⎝ ∂T ⎠ p since for an isobaric, non-flow process dq = dh = c p dT
•
•
Enthalpy variations in an ideal gas with constant specific heats • if the system is a perfect gas with constant specific heats h = u + p v = u + R T = (c v + R )T
•
if cp is also constant,
cp =

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