Final answer:
The final temperature of 500 g of water after losing 8000 cal of heat would be 74°C. This is calculated using the specific heat capacity of water (1 cal/g°C) to determine the temperature change, which is subtracted from the initial temperature.
Step-by-step explanation:
To calculate the final temperature of 500 g of water after losing 8000 cal of heat, we use the specific heat capacity of water, which is 1 cal/g°C. The specific heat capacity tells us how much heat is required to raise the temperature of one gram of a substance by one degree Celsius.
We start by considering the amount of heat lost (q), the mass of water (m), its specific heat capacity (C), and the change in temperature (ΔT), according to the formula:
q = m × C × ΔT
By rearranging the formula to solve for ΔT, we get:
ΔT = q / (m × C)
Substituting the known values:
ΔT = 8000 cal / (500 g × 1 cal/g°C) = 16°C
This means the water's temperature will decrease by 16°C. Therefore, the final temperature of the water is:
90°C - 16°C = 74°C