# How much heat to raise the temperature?

Everyone knows it takes heat to raise the temperature of something, whether it’s the air in your house or a kettle on the stove. If you want to design heat engines or use solar power to elevate the temperature of something, it helps if you can determine how much heat you need.

To begin with I’ll skip phase changes and just look at heating things that stay in the same phase—solid, liquid, or gas.

The basic equation is:

Q=mc(deltaT)

where:

Q = heat (units: cal, kcal, Joules, ft-lb, Btu, or kWhr)

m= mass (units: kg or lb)

c= specific heat for the particular material and temperature (units:kJoules/(kg-degC) or Btu/(lb-degF)

deltaT = change in temperature (units: degC, or degF)

To use the above equation correctly you need to make sure you use consistent units.

Below is a table that contains specific heats for various materials at 20 deg C. If you need other materials you can probably find them on the web or in handbooks for engineering, physics, or chemistry. Note that the values change with temperature and may change greatly when the substance goes through a phase change. These values are also for constant pressure. If you heat or cool at constant volume there are other numbers to use and I’ll discuss that at a later date.

 Material Specific heat at one atmosphere, kJ/(kg-degC) Specific heat at one atmosphere, Btu/(lb-degF) Air 1.02 0.24 Water 4.18 1.00 Steam (110 deg C) 2 0.48 Aluminum 0.9 0.22 Iron, Steel 0.45 0.11 Wood (pine) 2.8 0.67 Copper 0.39 0.09 Glass 0.84 0.20 Lead 0.13 0.03

I’ll give a few examples:

You want to raise the temperature of 1.5 pounds of aluminum by 50 degF then you’ll need:

Q=1.5lb x 0.22 Btu/(lb-degF) x 50 degF = 16.5 Btu of heat

You want to raise the temperature of 0.1kg of air by 100 degC

Q=0.1kg x 1.02kJ/(kg-degC) x 100degC = 10.2kJ

A few useful conversions:

1kw-hr = 3412 Btu

1 kw-hr = 3600 kJ,

1Btu=1.055kJ

Sources:

Marks’ Handbook for Mechanical Engineers, tenth edition

General Physics, 1984, Giancoli, Douglas