Question

178g of boiling water (temperature 378k, heat capacity 4.2j/g/k) are poured into an aluminum pan whose mass is 1470g and initial temperature 330k (the heat capacity of aluminum is 0.9j/g/k). What will be the final temperature of the system?

Answer 1

To find the final temperature of the water and the aluminum pan, calculate the heat lost by the water and the heat gained by the pan, then equate the two and solve for the final temperature.

Step-by-step explanation:

We are given 178g of boiling water at a temperature of 378K and an aluminum pan with a mass of 1470g at a temperature of 330K. To find the final temperature of the system, we equate the heat lost by the water to the heat gained by the pan. Using the formula Q = mcΔT, where 'Q' is the heat transfer, 'm' is the mass, 'c' is the specific heat capacity, and ΔT is the change in temperature, we set the heat transfer for water equal to the heat transfer for aluminum. Assuming no heat is lost to the surroundings, the final temperature can be calculated using the following equations:

Qwater = (mass of water) × (specific heat of water) × (change in temperature of water)
Qpan = (mass of the pan) × (specific heat of the pan) × (change in temperature of the pan)
Qwater = Qpan

To solve for the final temperature (Tfinal):

1. Calculate Qwater: Qwater = 178g × 4.2J/g/K × (Tfinal - 378K)
2. Calculate Qpan: Qpan = 1470g × 0.9J/g/K × (Tfinal - 330K)
3. Equate the two to find Tfinal: 178g × 4.2J/g/K × (Tfinal - 378K) = 1470g × 0.9J/g/K × (Tfinal - 330K)

Solving the above equation will give the final temperature of the system.