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 Tf . 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
Qgain =m2s2 (Tf – T2)
Qlost= m1s1 (Tf – T1)
Here s1 and s2 specific heat capacity of hot sample and water respectively.
So we can write
m2s2 (Tf – T2) = − m1s1 (Tf – T1)
m2s2Tf – m2s2T2= − m1s1Tf + m1s1T1
m2s2Tf + m1s1Tf = m2s2T2 + m1s1T1
The final temperature
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.
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.
Tf = 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.