Calorimetry

Calorimetry

Calorimetry means the measurement of the amount of heat released or absorbed by thermodynamic system during the heating process. When a body at higher temperature is brought in contact with another body at 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 mathematically expressed as

Heat gained or lost is measured with a calorimeter. Usually the calorimeter is an insulated container of water as shown in Figure 8.9.

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 hot sample is equal to heat gained by the water. It is shown in the Figure 8.10

Note the sign convention. The heat lost is denoted by 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

EXAMPLE 8.7

If 5 L of water at 50°C is mixed with 4L of water at 30°C, what will be the final temperature of water? Take the specific heat capacity of water as 4184 J kg^-1K^-1.

Solution

We can use the equation

m₁ = 5L = 5kg and m₂= 4L = 4kg, s₁ = s₂ and T₁=50°C =323K and T₂ = 30°C=303 K.

So

T_f = 314.11 K-273K ≈ 41°C.

Suppose if we mix equal amount of water (m₁ = m₂) with 50°C and 30°C, then the final temperature is average of two temperatures.

Suppose if both the water are at 30°C then the final temperature will also 30°C. It implies that they are at equilibrium and no heat exchange takes place between each other.