A 60g piece of ice at an intial temperature that is unknown is placed into a glass of 250g of water sitting at room temperature when it is 80 degrees F in the room. The glass and ice come up thermal equilibrium at 4 degrees Celsius.
What is the original temperature of the water in degrees Celsius?
Assuming that no heat is lost to the surroundings, find the intial temperature of the ice. Assume cice=200 J/kg* C and Lf=33.5.10^4 J/kg
To find the original temperature of the water in degrees Celsius, we can use the principle of conservation of energy. The heat lost by the water equals the heat gained by the ice during thermal equilibrium.
First, let's calculate the amount of heat gained by the ice. The specific heat capacity of ice, c_ice, is given as 200 J/(kg·°C), and the latent heat of fusion, L_f, is given as 33.5 × 10^4 J/kg.
The mass of the ice, m_ice, is 60 g = 0.06 kg.
The temperature change of the ice, ΔT_ice, is the final temperature (4 °C) minus the unknown initial temperature.
The heat gained by the ice can be written as:
Q_ice = (m_ice * c_ice * ΔT_ice) + (m_ice * L_f)
Next, let's calculate the heat lost by the water. The mass of the water, m_water, is given as 250 g = 0.25 kg.
The temperature change of the water, ΔT_water, is the final temperature (4 °C) minus the desired initial temperature.
The heat lost by the water can be written as:
Q_water = m_water * c_water * ΔT_water
Since there is no heat loss to the surroundings, the heat gained by the ice must be equal to the heat lost by the water:
Q_ice = Q_water
Therefore, we can set up the equation:
(m_ice * c_ice * ΔT_ice) + (m_ice * L_f) = m_water * c_water * ΔT_water
Now, we can solve for the initial temperature of the water, T_water_initial.
First, determine the change in temperature for both the ice and water:
ΔT_ice = 4 °C - T_water_initial
ΔT_water = 4 °C - T_water_initial
Substituting these values into the equation, we get:
(0.06 kg * 200 J/(kg·°C) * (4 °C - T_water_initial)) + (0.06 kg * 33.5 × 10^4 J/kg) = 0.25 kg * c_water * (4 °C - T_water_initial)
Now, we can solve this equation for T_water_initial to find the original temperature of the water in degrees Celsius.