10 kg of ice at -4 C is dropped into 15.1 kg of water at 36 C. What is the final temperature of the mixture?
T_final =
To calculate the final temperature of the mixture, we can use the principle of conservation of energy.
First, we need to determine the amount of heat gained or lost by each substance. The formula to calculate the heat gained or lost is:
Q = mcΔT
Where:
Q = heat gained or lost (in Joules)
m = mass of the substance (in kg)
c = specific heat capacity of the substance (in J/kg°C)
ΔT = change in temperature (in °C)
Let's calculate the heat gained or lost for each substance:
For the ice:
m_ice = 10 kg (mass of ice)
c_ice = 2100 J/kg°C (specific heat capacity of ice)
ΔT_ice = T_final - (-4°C) (change in temperature for ice)
Q_ice = m_ice * c_ice * ΔT_ice
For the water:
m_water = 15.1 kg (mass of water)
c_water = 4186 J/kg°C (specific heat capacity of water)
ΔT_water = T_final - 36°C (change in temperature for water)
Q_water = m_water * c_water * ΔT_water
According to the principle of conservation of energy, the heat gained by the water equals the heat lost by the ice when they reach thermal equilibrium. Therefore, we can write the equation:
Q_ice = -Q_water
Now, let's plug in the values and solve for T_final:
m_ice * c_ice * ΔT_ice = -m_water * c_water * ΔT_water
10 kg * 2100 J/kg°C * (T_final - (-4°C)) = -15.1 kg * 4186 J/kg°C * (T_final - 36°C)
Solving this equation will give us the final temperature of the mixture, T_final.