In the laboratory a "coffee cup" calorimeter, or constant pressure calorimeter, is frequently used to determine the specific heat of a solid, or to measure the energy of a solution phase reaction. A student heats 69.12 grams of tungsten to 98.93 °C and then drops it into a cup containing 85.45 grams of water at 23.82 °C. She measures the final temperature to be 25.63 °C. The heat capacity of the calorimeter (sometimes referred to as the calorimeter constant) was determined in a separate experiment to be 1.56 J/°C. Assuming that no heat is lost to the surroundings calculate the specific heat of tungsten.

As they indicate that there are no losses with the medium, the heat transferred by the tungsten is equal to the heat absorbed by the water plus the calorimeter

Q assigned = QAbsorbed

Q hot = Q cold + Q calorimeter

The mass of tungsten (m₁ = 69.12 10⁻³ kg) with an initial temperature (T₁ = 98.93°C),

The mass of water (m₂ = 85.45 10⁻³ kg) at a temperature (T₂ = 23.82°C),

a calorimeter constant (C = 1.56 J/ °C)

m₁ [tex]c_{e1}[/tex] (T₁ - [tex]T_{f}[/tex]) = (m₂ [tex]c_{e2}[/tex] + C) ([tex]T_{f}[/tex] - T₂)

[tex]c_{e1}[/tex]= (m₂ ce2 + C) ([tex]T_{f}[/tex]-T₀) / (m₁ (T₁-[tex]T_{f}[/tex])

[tex]c_{e1}[/tex] = (85.45 10-3 4186 + 1.56) (25.63 - 23.82) / (69.12 10-3 (98.93 - 25.63))

[tex]c_{e1}[/tex] = (357.69 + 1.56) 1.81 / (69.12 10-3 73.3)

[tex]c_{e1}[/tex] = 650.24 / 5.0665

[tex]c_{e1}[/tex] = 128.3 J / kg ° C