Re: Entropy Change Problem

[Bob Sciamanda <trebor@VELOCITY.NET>]

Consider that since you end up with two items in contact and at different
temperatures, the transition has not been toward equilibrium and therfore
not necessarilly toward an entropy increase (?)

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Polvani, Donald G." <donald_g_polvani@MD.NORTHGRUM.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, March 04, 2002 1:33 PM
Subject: Entropy Change Problem


> I'm having a problem getting the "right" answer to the following entropy
> change calculation.  I want the net entropy change when water freezes in
a
> surrounding gas:
>
> 1) Water at 0 deg C freezes slowly and isothermally.  I compute the
entropy
> change of this process (dS_ice) as -mL_f/T_0 where m is the mass of
water
> (or ice), L_f is the latent heat of fusion of water, and T_0 is the
freezing
> temperature (assumed constant).  The thermal energy given off by the
water
> as it freezes is mL_f  = delta_Q.
> 2) I assume a gas in a fixed volume, perfectly insulated container
encloses
> the ice.  I assume that the thermal energy given off by the water as it
> freezes is absorbed with no loss by the surrounding gas molecules.
> Therefore, the temperature of the gas increases above its assumed
initial
> temperature of T_0 by the amount delta_T with mL_f = nC_v delta_T =
delta_Q
> ,where n is the number of moles of gas present and C_v is the molar
specific
> heat of the gas at constant volume.  The entropy gain of the gas
(dS_gas) is
> given by the integral of dS = dQ/T as the temperature increases from T_0
to
> T_0 + delta_T.  This gives dS_gas = nC_v ln[(T_0 + delta_T)/T_0]
> 3) The net entropy gain of ice plus surrounding gas (after a little
> re-arranging) is dS_net = dS_ice + dS_gas = A [ln(1+x) - x]  where A = m
> L_f/delta_T and x = delta_T/T_0
>
> Unfortunately, ln(1+x) - x is < zero for all x > 0, so I have calculated
> that dS_net is < 0 rather than the answer I wanted (> 0)
>
> Would appreciate your help in finding my error or errors.
>
> Don Polvani
> Anne Arundel Community College