Given 400.0 g of hot tea at 80.0C, what mass of ice at 0C must bea added to obtain iced tea at 10.0C? The specific heat of water is 4.18 J/(g*C), The specific heat of water is 4.184 kJ/mol.
To solve this problem, we need to use the concepts of heat transfer and the specific heat capacity of water.
First, let's determine the amount of heat lost by the hot tea. We can do this using the equation:
Q = m * c * ΔT
Where:
Q is the heat lost (or gained) by the substance
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
In this case, the hot tea is losing heat, so we can calculate the heat lost from the tea using:
Q_1 = m_1 * c * (T_initial - T_final)
Where:
Q_1 is the heat lost by the tea
m_1 is the mass of the tea (400.0 g)
c is the specific heat capacity of water (4.18 J/(g*C))
T_initial is the initial temperature of the tea (80.0 C)
T_final is the final temperature of the tea (10.0 C)
Now, let's determine the amount of heat gained by the ice. We can use the equation:
Q_2 = m_2 * c * ΔT
In this case, the ice is gaining heat, so we can calculate the heat gained by the ice using:
Q_2 = m_2 * c * (T_final - T_initial)
Where:
Q_2 is the heat gained by the ice
m_2 is the mass of the ice (which we need to find)
c is the specific heat capacity of water (4.18 J/(g*C))
T_initial is the initial temperature of the ice (0.0 C)
T_final is the final temperature of the ice (10.0 C)
Since the total heat lost by the tea is equal to the total heat gained by the ice (assuming no heat loss to the surroundings), we can equate Q_1 and Q_2:
m_1 * c * (T_initial - T_final) = m_2 * c * (T_final - T_initial)
Substituting the known values:
(400.0 g) * (4.18 J/(g*C)) * (80.0 C - 10.0 C) = m_2 * (4.18 J/(g*C)) * (10.0 C - 0.0 C)
Now, let's solve for m_2:
m_2 = [(400.0 g) * (4.18 J/(g*C)) * (70.0 C)] / [(4.18 J/(g*C)) * (10.0 C)]
m_2 = 2800 g
Therefore, you must add 2800 grams of ice at 0.0°C to obtain iced tea at 10.0°C.