# How can heat and temperature affect engineering problems?

In our previous article, we looked at how pressure in fluids can affect engineering problems. In this article, we’re going to look into heat and temperature and how they affect engineering problems.

## Heat and temperature

Heat is a type of energy, measured in Joules J. When heat energy is applied to a substance, it results in a change to the temperature of that substance. Temperature is measured in degrees of celsius (°C), fahrenheit (°F) or Kelvins (K).

We need to recognise the difference between heat as a form of energy and temperature as a property. For example, to raise the temperature of a block of metal by 50 °C, will require x number of Joules. To heat a second block (of the same material type) with double the volume by 50 °C will require 2x joules. The temperature of the two blocks are the same, but the heat energy required is different.

## Temperature Scales

The celsius scale was derived around the freezing and boiling points of water, so that water freezes at 0°C (liquid to solid – ice), and will boil at 100°C (liquid to gas—steam) (under normal atmospheric pressure).

The kelvin scale uses the same temperature intervals as the celsius scale (so the difference between the freezing and boiling points of water is still 100K), however, the scale instead starts at the lowest possible theoretical temperature, 0K.

At 0K, there is theoretically zero energy within a substance. I.e., the atomic particles do not move. This point is equivalent to -273.15 °C (often estimated at -273 °C). This is the lowest possible temperature in the universe.

So to convert from °C to K, you simply add 273 °C.

Therefore, assuming atmospheric conditions,

- The freezing point of water is 0 °C, or 273 K
- The boiling point of water is 100 °C, or 373 K.

It is impossible for the temperature of any substance to be less than -273 °C.

## Specific Heat Capacity

Specific heat capacity is a material property which describes how easily or difficult a material can change temperature. It’s defined as the quantity of heat energy that we would need to apply to raise the temperature of a 1 kg block of material by 1 K (1 °C).

Therefore, the units are energy per mass, per temperature = J/(KgK) or J/(Kg°C) – both of which are identical. Specific heat capacity is often given the symbol, *c*. The specific heat capacity of some common materials are given below:

Material | Specific Heat Capacity, C (J/KgK) |

Air | 1000* |

Aluminium | 887 |

Brass | 920 |

Brick | 841 |

Cast Iron | 554 |

Concrete | 879 |

Copper | 385 |

Glass | 792 |

Gold | 130 |

Iron | 462 |

Magnesium | 1024 |

Platinum | 150 |

Rubber | 2005 |

Silicon | 710 |

Silver | 236 |

Stainless Steel 316 | 468 |

Titanium | 521 |

Tungsten | 133 |

Water | 4187 |

We can write the formula for specific heat capacity as c = Q/(MT), *where Q = Heat energy, M = mass of the material, and ΔT = change of temperature.*

Therefore, if we rearrange this to find the energy needed to raise the temperature of a material, we get:

Q = cMT or Q = cM(T2-T1), *where T _{2} is the final temperature and T_{1} is the starting temperature.*

Let’s look at an example. We’ll work out how much energy is needed to raise the temperature of a 2 kg block of aluminium from 20°C to 90°C. We’ll use our equation Q = cM(T2-T1). From the table above, we can see that the heat capacity of aluminium is 887 J/kgK.

This gives us:

Q = 887 2(90-20) = 887270

Q = 124,180J = 124 KJ

## Changes of state and latent heat

We’ve so far been using the equation [Q = cM(T2-T1)], which makes the assumption that the material has not changed state during the heating process. In other words, the aluminium block in our example started and finished as a solid.

However, if enough heat energy is applied or lost, the material can change state between a solid, liquid, or gas. We all know that if we take a block of ice at -30°C, apply some heat, then once the ice reaches 0°C it will turn into liquid water. Continue to heat this water to beyond 100 °C and it will turn into steam, a gas.

Below are typical graphs of what happens to ice when you heat it (fig.1 ) and what happens to steam when you cool it (fig 2).

Notice how the line is not a straight line, i.e. it does not follow the equation Q = cM(T2-T1) at the points at which you get a change of state.

At the points where the substance changes state, you get no temperature rise despite heat energy still being applied, this is termed latent heat.

Keep an eye out for our next article looking into how continuity can affect engineering problems.

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