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)?

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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)?

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Answer 1 · 2017-06-24T00:58:23

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
$~~9 xx10^5 "Joules"$ = $900 Kj$

Answer 2 · 2017-06-24T01:55:46

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:

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:

[

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.

Answer 3 · 2017-06-24T21:37:21

Thermal history of cooling cast iron

Explanation:

Thermal history of cooling cast iron from $1500^oC$ to $25^oC$ ...
enter image source here

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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

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