Ice cubes of total mass 6.00 grams have temperature -4.0°C. Then they are placed in 50.0 grams of water at 20.0°C in an insulated foam cup. What is the equilibrium temperature of the water inside the cup?
To find the equilibrium temperature of the water inside the cup, we can use the principle of conservation of energy. The energy lost by the ice cubes as they warm up will be equal to the energy gained by the water as it cools down.
First, let's calculate the energy lost by the ice cubes. We can use the specific heat capacity formula:
Q = m * c * ΔT
Where:
Q is the energy lost by the ice cubes
m is the mass of the ice cubes
c is the specific heat capacity of ice
ΔT is the change in temperature of the ice cubes
The specific heat capacity of ice is 2.09 J/g°C, and the change in temperature for the ice cubes is given by:
ΔT = 0°C - (-4.0°C) = 4.0°C
Plugging these values into the formula:
Q = 6.00 g * 2.09 J/g°C * 4.0°C
Q = 50.16 J
Next, let's calculate the energy gained by the water. We can use the same formula, but with the specific heat capacity of water, which is 4.18 J/g°C, and the change in temperature for the water is:
ΔT = 20.0°C - T (T is the equilibrium temperature of the water)
Plugging these values into the formula:
Q = 50.0 g * 4.18 J/g°C * (20.0°C - T)
Q = 2090 J - 209 J*T
Now, according to the principle of conservation of energy, the energy lost by the ice cubes is equal to the energy gained by the water:
50.16 J = 2090 J - 209 J*T
Rearranging the equation to solve for T:
209 J*T = 2090 J - 50.16 J
209 J*T = 2039.84 J
T = 9.77°C
Therefore, the equilibrium temperature of the water inside the cup is approximately 9.77°C.