Question

Calculate the final temperature when 54 mL of water at 60 ∘C are added to 30 mL of water at 20 ∘C .

Answer 1

To calculate the final temperature when mixing two substances at different temperatures, we can use the principle of energy conservation. By using the equation Q = mcΔT, we can calculate the heat gained or lost by each substance and set up an equation to solve for the final temperature. In this case, the final temperature will be approximately 43.4°C.

Step-by-step explanation:

To calculate the final temperature when mixing two substances at different temperatures, we can use the principle of energy conservation. This principle states that the total heat gained by one substance must be equal to the total heat lost by the other substance.

1. First, we need to calculate the amount of heat gained or lost by each substance using the equation Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
2. Since the final temperature will be the same for both substances, we can set up an equation using the heat gained or lost by each substance: m₁c₁(T - T₁) + m₂c₂(T - T₂) = 0, where m₁ and m₂ are the masses, c₁ and c₂ are the specific heat capacities, T₁ and T₂ are the initial temperatures, and T is the final temperature.
3. By substituting the given values into the equation, we can solve for T. In this case, the mass of water 1 is 54 mL, the mass of water 2 is 30 mL, the specific heat capacity of water is 4.18 J/g°C, the initial temperature of water 1 is 60°C, and the initial temperature of water 2 is 20°C.

After performing the calculations, the final temperature will be approximately 43.4°C.