Question

When a 290-g piece of iron at 180 ∘c is placed in a 95-g aluminum calorimeter cup containing 250 g of glycerin at 10 ∘c, the final temperature is observed to be 38 ∘c. Estimate the specific heat capacity of glycerin. The specific heat capacity of iron is 450 J/(kg K), and that of aluminium is 900 J/(kg K).

Answer 1

The specific heat capacity of glycerin can be estimated using the principle of conservation of energy. By equating the heat gained by the glycerin and calorimeter to the heat lost by the iron, we can calculate the specific heat capacity of glycerin. The specific heat capacity of glycerin is approximately 3.8 J/(g K).

Step-by-step explanation:

The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of a unit mass of the substance by one degree Celsius or Kelvin.

To estimate the specific heat capacity of glycerin, we can use the principle of conservation of energy. The heat gained by the glycerin and the calorimeter cup must be equal to the heat lost by the iron.

Using the equation Q = mcΔT, where Q is the heat gained or lost, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature, we can calculate the specific heat capacity of glycerin.

1. Calculate the heat lost by the iron: Qiron = mcΔT = (290 g)(450 J/(kg K))(38 °C - 180 °C)
2. Calculate the heat gained by the glycerin: Qglycerin + Qcalorimeter = mcΔT = (250 g)(c)(38 °C - 10 °C)
3. Set the two equations equal to each other and solve for c

Plugging in the given values and solving for c, we find that the specific heat capacity of glycerin is approximately 3.8 J/(g K).