THERMO Spoken Here! ~ J. Pohl © ( A0300) | ( A1040 - ) |
The guns of the German Battleship, Bismarck (1933 - 1941), fired shells weighing about 760kg a distance of 20 miles. The rifles were constructed of "specialty steel."
Fabrication of such barrels begins with a cupola containing enough pure molten for a barrel. Carbon at about two percent by mass is mixed into the iron. The iron/carbon mixture was then poured into a pre-constructed ceramic mold. Upon solidifying, this preliminary barrel is broken from the mold and and cooled. This solid (but relatively soft) iron/carbon mixture is machined to tolerances.
The final step, heat treatment, transforms the iron and carbon into steel. The barrel is placed in a coal furnace and heated cherry-red to a temperature of 1300°C. Upon removal from the furnace the barrel is quenched by lowering it endwise into a shaft-shaped pool of oil. The gun barrel length was 19.6 meters, bored 38 centimeters in diameter with an average outside diameter of 68 centimeters. The circular quench pool, 26 meters deep, contains oil at 25°C. The barrel is lowered to become completely submerged, the shaft is full to ground-level.
Rapid cooling freezes the steel and carbon molecules into a high-strength configuration. The table below provides properties for the steel (approximate as iron) and oil.
Normal Properties | |||||||
ρ (STP phase) (kg/m3) |
cp,avg (sol) (J/gK) |
Tmp (°C) |
hsf (J/gK) |
cp,avg (liq) |
Tnbp (°C) |
hfg (J/g) |
|
Iron | 7,890 ~ (sol) | 0.35 ~(sol) | NA | NA | NA | NA | NA |
Oil | 812 ~ (liq) | 0.39 cal/gC~(liq) | NA | NA | 194kcal/kg | 209 | 0.402kcal/kgC |
Immediately upon immersion, oil in contact with the rifle vaporizes and explodes into flames. Though suppressed by a blanket of nitrogen, an ideal quench pool needs (more than) enough oil so its temperature in the adiabatic quench gets no higher than 180°C. In addition quench is adequate when the barrel temperature becomes 800°C.
i) Calculate the least mass of oil required.
ii) What diameter.
ΔU = - ∫patmdV + ∑Q
But pressure being constant this becomes:
Δ(U + pV) = ∑Q
ΔH = ∑Q
The steel barrel comes out of the furnace as a solid. In cooling, there will be no phase change. Being a solid-to-solid event, enthaply is expanded as shown. Also notice only "one" heat (form the barrel to surroundings) is relevant:
(m cp,avg)steel(T2 - T1) = Q1-2
Insert the stated temperatures
mcp,avg,steel(600 - 1200)°C = Q1-2
We see three unknown quantities. The mass of the barrel is readily calculated.
mbarrel = ρV, thus m = xxx kg
XXX kg ( cp,avg,steel)(600 - 1200)°C = Q1-2We have arrived at a single equation with two unknown quantities which are the average specific heat of the event and the event heat. We need another equation that has an unknown but one that is eithewr the average specific heat or the event heat.
Tabular Data are in fact equations. Our material is steel. The pure substance closest in properties to steel is iron. Below is a small table of normal properties of iron.
Note: In reading any compilation of data, one needs to realize that data are measured in order of importance first. Importance mean properties of commercial importance are determined, often at considerable expense. Generally, properties not listed are those rarely needed in manufacturing or engineering. Thus some entries in tables of clooected substances are notated "?" not to mean that the quantity is mysterious but just to mean there hase been not economic reason to measure this. Occasionally in esoteric literature, the letters NA (not applicable) fill the vacant box, meaning "you will not need this property in rope manufacture.
The property datum that, Tmp = 1540°C, confirms our assumption that the barrel, initially (1200°C) was solid.