Determine the final temperature of a system, if 120 grams had an initial temperature of 80°C and mixes with 3,000 g of water at an initial temperature of 20°C

The final temperature of the mixture is 22.3°C

Explanation:

Assuming that the 120 g substance at 80°C is water, final temperature of the mixture can be determined using the formula:

Heat lost = Heat gained

Heat = mc∆T where m is mass, c is specific heat capacity of water, and ∆T is the temperature change = Tfinal - Tinitial.

Let the final temperature be T

Heat lost = 120 × c × (T - 80)

Heat gained = 3000 × c × ( T - 20)

Equating the heat lost and heat gained

120 × c × -(T - 80) = 3000 × c × (T - 20)

9600 - 120T = 3000T - 60000

60000 + 9600 = 3000T + 120T

69600 = 3120T

T = 69600/3120

T = 22.3°C

Therefore, the final temperature of the mixture is 22.3°C