Molten iron is extremely hot, averaging about 1,500 C. The specific heat of iron is 0.46 J/gC. How much heat is released to the atmosphere when 1 kg molten iron cools to room temperature (25 C)?

3 Answers
Jun 24, 2017

Answer:

900 Kj

Explanation:

Since the type of iron is not specified then it is assumed to be 'Cast Iron' which has a melting point of 1204 deg-Celsius*.
*http://www.onlinemetals.com/meltpt.cfm

The total heat transfer would be ,,,

#Q_"Total = "Sigma (Q_("molten") + Q_("freezing") + Q_("cooling"))#
..............................................................................................................................
=> #Q_"molten"=(mcDeltaT)_"molten" #
= #(1000gxx0.18"J/g"^oCxx(1500 - 1204)^oC) =53,280# Joules

(Specific Heat of Molten Iron) http://www.engineeringtoolbox.com/liquid-metal-boiling-points-specific-heat-d_1893.html
..............................................................................................................................
=> #Q_"freezing"=(mDeltaH_f)_"freezing"#
= #(1000gxx272J/g) = 272,000# Joules

(Heat of Fusion of Molten Iron) http://www.engineeringtoolbox.com/fusion-heat-metals-d_1266.html

...............................................................................................................................
=> #Q_"cooling"=(mcDeltaT)_"cooling"to""25^oC"#
= #(1000gxx0.46J/g^oCxx(1204 - 25)^oC)# = 542,340 Joules

(Specific Heat of Iron (s) = 0.46 #J/g^oC# as given in problem data)
..............................................................................................................................
#Q_"Total" = (53,280 + 272,000 + 542,340)J# = 867,620 Joules
#~~9 xx10^5 "Joules"# = #900 Kj#

Jun 24, 2017

I got #"1020 kJ"# were RELEASED into the atmosphere, ignoring phase changes between the #alpha#, #delta#, and #gamma# phases and just looking at the temperature changes.

You can get more context here:
https://en.wikipedia.org/wiki/Iron#Phase_diagram_and_allotropes

and you can examine the specific heat capacity variations more closely here:
http://webbook.nist.gov/cgi/cbook.cgi?ID=C7439896&Mask=2&Type=JANAFS&Plot=on#JANAFS

On another note, this #"1020 kJ"# is quite a bit higher than what one would normally expect to get, #"655.5 kJ"#, due to taking into account the huge variation in heat capacity across #1475^@ "C"#.

If you simply assume a #C_P# of #"0.46 J/g"cdot"K"# throughout, you would get #"655.5 kJ"# instead (#656# to three sig figs).


There is a HUGE assumption here that iron's specific heat capacity doesn't change from #25^@ "C"# to #1500^@ "C"#, which is clearly not true. Here is the phase diagram of iron:

https://upload.wikimedia.org/

Since all these phases at #"1 bar"# are solids, we are safe in assuming there is no major enthalpy of solid-solid phase transitions to worry about.

However, the specific heat capacity #C_P# at constant pressure changes drastically as we transition through #alpha#, #gamma#, and #delta# phases:

[http://webbook.nist.gov/

The wonky curve is the #alpha# and #delta# phase, and the linear curve is the #gamma# phase. Here's how I would treat this:

  • #alpha#-phase, from #"298.15 K"# up to #"700 K"# (#426.85^@ "C"#), using an average of #C_P ~~ "29.656 J/mol"cdot"K"# (at #~~ "500 K"#), or #"0.531 J/g"cdot"K"#.
  • #alpha#-phase, from #"700 K"# to #"935 K"# (#661.85^@ "C"#) using an average of #C_P ~~ "40.149 J/mol"cdot"K"# (at #~~ "816 K"#), or #"0.719 J/g"cdot"K"#
  • #alpha#-phase, from #"935 K"# to #"1042 K"# (#768.85^@ "C"#) using an average of #C_P ~~ "59.442 J/mol"cdot"K"# (at #~~ "1010 K"#), or #"1.064 J/g"cdot"K"#
  • #alpha#-phase, from #"1042 K"# to #"1100 K"# (#826.85^@ "C"#) using an average of #C_P ~~ "65.743 J/mol"cdot"K"# (at #~~ "1068 K"#), or #"1.177 J/g"cdot"K"#
  • #alpha#-phase, from #"1100 K"# to #"1183.15 K"# (#910^@ "C"#, the #alpha->gamma# transition temperature) using an average of #C_P ~~ "43.029 J/mol"cdot"K"# (at #~~ "1150 K"#), or #"0.770 J/g"cdot"K"#
  • #gamma#-phase, from #"1183.15 K"# to #"1667.15 K"# (#1394^@ "C"#, the #gamma->delta# transition temperature) using an average of #C_P ~~ "35.856 J/mol"cdot"K"# (at #~~ "1420 K"#), or #"0.642 J/g"cdot"K"#
  • #delta#-phase, from #"1667.15 K"# to #"1773.15 K"# (#1500^@ "C"#!), using an average of #C_P ~~ "41.764 J/mol"cdot"K"# (at #~~ "1722 K"#), or #"0.748 J/g"cdot"K"#.

Aren't you glad we aren't doing phase changes? :-)

So, we would have the heat of cooling as the negative of the heat of heating:

#q_"cool" = -(q_1 + . . . + q_7)#

#= -m(C_(P1)DeltaT_(0->1) + . . . + C_(P7)DeltaT_(6->7))#

I'll leave the units out, but you know that they are #"J/g"cdot"K"# for #C_P# and #"K"# for #T#. The mass is in #"g"#.

#= -1000 cdot [0.531(700 - 298.15) + 0.719(935 - 700) + 1.064(1042 - 935) + 1.177(1100 - 1042) + 0.770(1183.15 - 1100) + 0.642(1667.15 - 1183.15) + 0.748(1773.15 - 1667.15)]#

Each phase then approximately contributes:

#= overbrace(-"628487 J")^(alpha" phase") + overbrace(-"310728 J")^(gamma" phase") + overbrace(-"79288 J")^(delta" phase")#

#~~# #-1.020 xx 10^(6)# #"J"#,

or about #color(blue)(-"1020 kJ")#, to three sig figs.

Jun 24, 2017

Answer:

Thermal history of cooling cast iron

Explanation:

Thermal history of cooling cast iron from #1500^oC# to #25^oC# ...
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