Determine the final temperature after 52.5 g of copper (c = 0.385 J/g  C) at 93.6  C is placed into 225 g of water at 21.3  C.

22.82°C

Explanation:

Concept tested: Quantity of heat

We are given;

Mass of copper = 52.5 g Specific heat capacity of copper = 0.385 J/g°C Initial temperature of copper = 93.6 °C Mass of water = 225 g Initial temperature of water = 21.3°C

We are required to calculate the final temperature of the mixture.

To answer the question we are going to assume the final temperature is X°C. Then we can use the following simple steps; Step 1: Calculate the amount of heat released by copper;

Q = m * c * ΔT

Since the final temperature is X°C then the change in temperature, ΔT will be (93.6 - X) °C

Quantity of heat released by copper, Q will be;

= 52.5 g * 0.385 J/g°C * (93.6 - X) °C

= 1891.89 - 20.2125X joules

Step 2: Amount of heat gained by water

Specific heat capacity of water = 4.184 J/g°C

Change in temperature = (X-21.3) °C

Therefore;

Q = 225 g * 4.184 J/g°C * (X-21.3) °C

= 941.4X-20051.82 Joules

Step 3: Calculate the final temperature

We know that the quantity of heat released is equivalent to the amount of heat absorbed.

Therefore;

1891.89 - 20.2125X Joules = 941.4X-20051.82 Joules

961.6125X = 21943.71

X = 22.82°C

Therefore, the final temperature is 22.82°C