The final temperature of the metal and water is 75.6 ⁰C.
How to calculate the final temperature of the mixture?
The final temperature of the metal and water is calculated by applying the principle of conservation of energy.
Heat obtained by the water equals heat lost by the metal.
The following is the formula for heat capacity:
Q = mcΔθ
where;
- m is the mass of the metal
- c is the specific heat capacity
- Δθ is the change in temperature
The final temperature of the metal and water is calculated as;
1 kg x 500 J/kgC x (98 - T) = 0.05 kg x 4186 J/kgC x (T - 22)
49,000 - 500T = 209.3T - 4,604.6
49,000 + 4604.6 = 209.3T + 500T
709.3 T = 53,604.6
T = 53,604.6 / 709.3
T = 75.6 ⁰C
The complete question is below:
A 1.0 kg sample of metal with a specific heat of 0.50 KJ/KgC is heated to 98 ⁰C and then placed in a 50.0 g sample of water at 22 ⁰C. What is the final temperature of the metal and the water?