Question

If 37.0g of an unknown mixture with a specific heat capacity of 2.53 J/g°C at 40.0°C is mixed with 50.0g of another unknown mixture having a specific heat capacity of 3.44 J/g°C at 20.0°C, what is the final temperature of the mixture?

A. 30.0°C
B. 32.5°C
C. 35.0°C
D. 37.5°C

Answer 1

The question involves calculating the final temperature of two different mixtures with known masses and specific heat capacities when mixed. By setting up the heat exchange equations and applying the principle of conservation of energy, we can determine that the final temperature of the mixture is 32.5°C (Option B).

Step-by-step explanation:

To find the final temperature of two mixtures with different initial temperatures and specific heat capacities when they are mixed together, we can set up an equation based on the principle of conservation of energy. The heat lost by the hotter mixture will be equal to the heat gained by the cooler mixture. We'll use the formula q = mcΔT, where q is the heat absorbed or released, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

For the mixture at 40.0°C:
qhot = mhot × chot × (Tfinal - Tinitial,hot)

37.0 g × 2.53 J/g°C × (Tfinal - 40.0°C)

For the mixture at 20.0°C:
qcold = mcold × ccold × (Tfinal - Tinitial,cold)

50.0 g × 3.44 J/g°C × (Tfinal - 20.0°C)

Since no heat is lost to the surroundings, we have:
qhot + qcold = 0

Solving the equation will provide the final temperature of the mixture. We can rule out options A, C, and D, finding that option B (32.5°C) is the correct answer by substituting the options back into the equations and checking which one balances the equation (has equal amounts of heat exchange).