Equal masses of two different liquids have the same temperature of 25 °C. Liquid A has a freezing point of -23 °C and a specific heat capacity of 1,278 J/(kg C°). Liquid B has a freezing point of -75.6 °C and a specific heat capacity of 3,361 J/(kg C°). The same amount of heat must be removed from each liquid in order to freeze it into a solid at its respective freezing point. Determine the difference L f,A - L f,B between the latent heats of fusion for these liquids (J/kg).
To determine the difference in latent heats of fusion (L_f) between the two liquids, we need to first understand the concept of latent heat of fusion.
The latent heat of fusion is the amount of heat energy required to change a substance from its solid state to its liquid state (or vice versa) at a constant temperature. It is often denoted by L_f and is measured in joules per kilogram (J/kg).
Given that the two liquids have equal masses and we need to remove the same amount of heat from each liquid to freeze it, we can assume that the quantity of heat removed is the same for both liquids.
Let's start with Liquid A:
- Freezing point of Liquid A = -23 °C
- Temperature of Liquid A = 25 °C
To calculate the heat that needs to be removed from Liquid A, we need to calculate the temperature change from 25 °C to -23 °C using its specific heat capacity (C):
Q_A = mass_A * C_A * (T_final - T_initial)
= mass_A * C_A * (T_A - T_initial)
= mass_A * C_A * (T_A - 25)
Similarly, for Liquid B:
- Freezing point of Liquid B = -75.6 °C
- Temperature of Liquid B = 25 °C
Q_B = mass_B * C_B * (T_B - 25)
Since the same amount of heat is removed for both liquids:
Q_A = Q_B
Now, let's calculate the specific latent heat of fusion for each liquid using the formula:
Q_A = mass_A * L_f,A
Q_B = mass_B * L_f,B
Since mass_A = mass_B:
L_f,A = Q_A / mass_A
L_f,B = Q_B / mass_B
Since Q_A = Q_B:
L_f,A = L_f,B
Therefore, the difference in latent heats of fusion (L_f,A - L_f,B) is 0.