Answer :
Final answer:
The final temperature of the mixture is approximately 24.52 degrees Celsius.
Explanation:
To find the final temperature of the mixture, we can use the principle of conservation of energy. The heat lost by the metal is equal to the heat gained by the water. The heat lost by the metal can be calculated using the formula:
Heat lost by the metal = mass of the metal * specific heat of the metal * change in temperature of the metal
The heat gained by the water can be calculated using the formula:
Heat gained by the water = mass of the water * specific heat of water * change in temperature of the water
Setting these two equations equal to each other and solving for the final temperature of the mixture gives:
Final temperature = ((mass of the metal * specific heat of the metal * change in temperature of the metal) + (mass of the water * specific heat of water * change in temperature of the water))/(mass of the metal * specific heat of the metal + mass of the water * specific heat of water)
Plugging in the given values:
Final temperature = ((50 g * 0.6 calorie per gram centimeter * (120 - final temperature)) + (1.6 kg * 4.18 Joule per gram centimeter * (final temperature - 25 degrees Celsius)))/(50 g * 0.6 calorie per gram centimeter + 1.6 kg * 4.18 Joule per gram centimeter)
Simplifying the equation gives:
Final temperature = (30(120 - final temperature) + 6692(final temperature - 25))/(30 + 6692)
Multiplying through by 30 + 6692:
Final temperature = 30(120 - final temperature) + 6692(final temperature - 25)
Expanding and simplifying the equation:
Final temperature = 3600 - 30final temperature + 6692final temperature - 167300
Combining like terms:
Final temperature = 6686 final temperature - 163700
Bringing the terms involving final temperature to one side:
6676 final temperature = 163700
Dividing both sides by 6676:
Final temperature = 24.52 degrees Celsius
Therefore, the final temperature of the mixture is approximately 24.52 degrees Celsius.
