heat_transfer

# heat_transfer - HEAT TRANSFER AND THE SECOND LAW Thus far...

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HEAT TRANSFER AND THE SECOND LAW Thus far we’ve used the first law of thermodynamics: Energy is conserved. Where does the second law come in? One way is when heat flows. Heat flows in response to a temperature gradient. If two points are in thermal contact and at different temperatures, T 1 and T 2 then energy is transferred between the two in the form of heat, Q. Heat Transfer and The Second Law page 1 © Neville Hogan

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The rate of heat flow from point 1 to point 2 depends on the two temperatures. ˙ Q = f(T 1 ,T 2 ) If heat flows from hot to cold, (the standard convention) this function must be such that ˙ Q > 0 iff T 1 > T 2 ˙ Q < 0 iff T 1 < T 2 ˙ Q = 0 iff T 1 = T 2 Heat Transfer and The Second Law page 2 © Neville Hogan
In other words, the relation must be restricted to 1st and 3rd quadrants of the ˙ Q vs. T 1 – T 2 plane. Q T 1 -T 2 . N OTE IN PASSING : It is not necessary for heat flow to be a function of temperature difference alone. —see example later. Heat Transfer and The Second Law page 3 © Neville Hogan

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HEAT FLOW GENERATES ENTROPY. F ROM THE DEFINITION OF ENTROPY : dQ = TdS Therefore ˙ Q = T ˙ S I DEALIZE THE HEAT TRANSFER PROCESS : Assume no heat energy is stored between points 1 and 2. Therefore ˙ Q = T 1 ˙ S 1 = T 2 ˙ S 2 Heat Transfer and The Second Law page 4 © Neville Hogan
N ET RATE OF ENTROPY PRODUCTION : entropy flow rate out minus entropy flow rate in. ˙ S 2 - ˙ S 1 = ˙ Q /T 2 - ˙ Q /T 1 = ˙ Q(T 1 - T 2 ) /T 1 T 2 Absolute temperatures are never negative (by definition). The product of heat flow rate and temperature difference is never negative. —due to the restrictions on the relation between heat flow rate and temperature ( ˙ Q > 0 when T 1 > T 2 etc.) T HEREFORE THE NET RATE OF ENTROPY PRODUCTION IS NEVER NEGATIVE . ˙ S 2 - ˙ S 1 0. Heat Transfer and The Second Law page 5 © Neville Hogan

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FURTHERMORE. .. In a heat transfer process, zero entropy production requires zero heat flow. This requires either a perfect thermal insulator ( ˙ Q = 0) or a zero temperature gradient (T 1 = T 2 ). These two constraints on the heat transfer process —non-negative entropy production —zero entropy production iff zero heat flow are consequences of the second law of thermodynamics. N
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## This note was uploaded on 02/27/2012 for the course MECHANICAL 2.141 taught by Professor Nevillehogan during the Fall '06 term at MIT.

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heat_transfer - HEAT TRANSFER AND THE SECOND LAW Thus far...

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