Final answer:
To find the final temperature of water after mixing with a glass at room temperature, we calculate the heat transfer using the specific heat capacities of water and glass and solve for equilibrium temperature using the conservation of energy.
Step-by-step explanation:
To calculate the final temperature of water in equilibrium after pouring 250 ml (250 g) of cold water at 4.0 degrees Celsius into a glass (200 g) that is at room temperature, we need to apply the concept of heat transfer and the principle of the conservation of energy. Since no external heat loss is considered, the heat lost by the glass will equal the heat gained by the water until thermal equilibrium is reached.
The specific heat capacity of water is 4.184 J/(g°C), and for typical glass, it is roughly 0.840 J/(g°C). The heat transfer equation Q = mcΔT can be used to set up the following:
Q(water) = mcΔ2T(water)
Q(glass) = mcΔ2T(glass)
Assuming the system reaches equilibrium at temperature T(f), we can set the two equations equal to each other because the heat lost by the glass will be equal to the heat gained by the water.
(m(water) x c(water) x (T(f) - T(initial water))) = (m(glass) x c(glass) x (T(initial glass) - T(f)))
Solving for T(f) would give us the final temperature. Now, using the provided temperatures for the initial conditions, we would replace the variables with:
(250 g x 4.184 J/g°C x (T(f) - 4°C)) = (200 g x 0.840 J/g°C x (20°C - T(f)))
This equation can then be solved for T(f) to find the final temperature of the system.