Question

Discuss the effect of each of these “experimental errors” on the calculated Cs, metal. EXPLAIN your reasoning.

a. A student measures the mass of the water+calorimeter before adding the metal, and right as the metal is dropped in, some water splashes out.

b. A student takes the metal out of the hot water bath,

c/and allows it to cool a little before placing it into the DI water in the calorimeter.

Answer 1

a. As per the principle of thermochemistry,

heat lost by the hot metal = heat gained by the cold water + heat gained by the calorimeter.

Let m be the mass of the metal and C_s is the specific heat of the metal. Let M be the mass of the water and C_w and C_c are the specific heats of water and the calorimeter. Let Δt and Δt’ be the temperature changes of the metal and the water plus calorimeter.’

Thus,

heat lost by the metal = m*C_s*Δt

heat gained by the water = M*C_w*Δt’

heat gained by the calorimeter = C_c*Δt’

By the principle of thermochemistry,

m*C_s*Δt = M*C_w*Δt’ + C_c*Δt’

=====> C_s = (M*C_w*Δt’ + C_c*Δt’)/(m*Δt)

Since some of the water splashes out of the calorimeter, M is lower than the actual value and thus the numerator in the above expression decreases. Consequently, the calculated specific heat of the metal, C_s will be lower than the actual value.

b. The hot metal is supposed to be dropped into the calorimeter containing the cold water immediately after the metal is withdrawn from the hot water. However, since the metal was cooled a little before introduction into the cold water, the temperature change, Δt for the metal will be lower than the true value. As per the above expression, the denominator decreases and hence, the calculated C_s will be higher.