Question

In an insulated cup of negligible heat capacity, 50g of water at 40 degrees Celsius is mixed with 30g of water at 20 degrees Celsius. The final temperature of the mixture is closest to:

a) 25°C
b) 30°C
c) 35°C
d) (Answer not provided)

Answer 1

To find the final temperature when mixing two substances, use the principle of conservation of energy and the formula for heat transfer. In this case, the final temperature of the mixture is closest to 35°C. (option c)

Step-by-step explanation:

To find the final temperature when mixing two substances, you can use the principle of conservation of energy and the formula for heat transfer. In this case, the heat lost by the warmer water is equal to the heat gained by the colder water. The equation for heat transfer is:

Q = mcΔT

where Q is the heat transfer, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the temperature change. By plugging in the values for each mass and initial temperature, we can calculate the final temperature of the mixture.

In this scenario, we have:

For 50g of water at 40°C: m1 = 50g, T1 = 40°C, and c = 4.184 J/(g•°C)

For 30g of water at 20°C: m2 = 30g, T2 = 20°C, and c = 4.184 J/(g•°C)

Using the formula, we find that the final temperature of the mixture is closest to 35°C.