SM090    Callendar’s apparatus for Mechanical Equivalent     circa 1950      Heat

  A friction band loaded with a mass on one end and a spring balance at the other end goes round a copper calorimeter that can be turned by hand.   The temperature rise of the calorimeter and water inside is proportional to the mechanical energy dissipated.

  If the radius of the calorimeter is r, the number of revolutions is n and T₂ –T₁ is the average tension of the friction band.   Also, if S is the specific heat of the calorimeter and water and  θ₂ - θ₁ + δθ is the corrected temperature rise, M being the mass of the calorimeter.   Then:

                                                    is the mechanical equivalent of heat in ergs/calorie.

In a typical experiment on apparatus SM090:

Mass of water in calorimeter was 75 grams

Mass of calorimeter 286 grams

Specific heat of copper, 0.1 calories/gram/deg C

Radius of calorimeter 3.80 cm

T₂ = 1000 g, T₁ = 125 g

Duration of temperature rise 5 minutes

Initial temperature = 26.06 deg C

Final temperature = 28.42 deg C

Number of revolutions 550

Rate of cooling 0.046deg C   per minute at maximum temperature reached

Cooling correction from above = 0.115 deg C   (cooling loss during half the time of experiment)

So corrected temperature rise is 2.48 deg C

Using the formula the mechanical equivalent of heat = 43.8 ergs per calorie

Since 1J = 1x10⁷ ergs, therefore mechanical equivalent of heat is 4.38 Joules/calorie

The standard result is 4.16 Joules/calorie.