Question

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)?

Answer 1

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

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

Thermal history of cooling cast iron

Explanation:

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