Question

Explain Calorimetry and derive an expression for final temperature when two thermodynamic systems are mixed.

Answer 1

Calorimetry: Calorimetry means the measurement of the amount of heat released or absorbed by the thermodynamic system during the heating process. When a body at a higher temperature is brought in contact with another body at a lower temperature, the heat lost by the hot body is equal to the heat gained by the cold body. No heat is allowed to escape to the surroundings. It can be Anomalous expansion of water in lakes mathematically expressed as

Q_gain = −Q_lost

Q_gain + Q_lost = 0

Heat gained or lost is measured with a calorimeter. Usually, the calorimeter is an insulated container of water. A sample is heated at high temperature (T₁) and immersed into water at room temperature (T₂) in the calorimeter. After some time both sample and water reach a final equilibrium temperature T_f. Since the calorimeter is insulated, heat given by the water.

  Calorimeter with sample of block

Q_gain = – Q_lost

Note the sign convention. The heat lost is denoted by a negative sign and heat gained is denoted as positive.

From the definition of specific heat capacity

Q_gain = m₂s₂ (T_f – T₂)

Q_lost = m₁s₁ (T_f – T₁)

Here s₁ and s₂ specific heat capacity of hot sample and water respectively.

So we can write

m₂s₂ (T_f – T₂) = − m₁s₁ (T_f – T₁)

m₂s₂T_f – m₂s₂T₂ = − m₁s₁T_f  + m₁s₁T₁

m₂s₂T_f + m₁s₁T_f = m₂s₂T₂ + m₁s₁T₁

The final temperature T_f = `("m"_1"s"_1"T"_1 + "m"_2"s"_2"T"_2)/("m"_1"s"_1 + "m"_2"s"_2)`