Emily makes 0.250 kg of hot tea at 99.0°C. How much ice at 0.00°C must she add to the tea so that the mixture reaches a final temp. of 8.00°C? (You may treat the tea as if its water.)
PLEASE HELP ASAP, I DO NOT KNOW HOW TO SOLVE THIS PROBLEM
sum of heats gained is zero.
heat gained by hot tea+heatgainedbyice+heat gained by icemelted=0
remember Heatgained by hot tea is negative.
To solve this problem, we can use the principle of conservation of energy. We know that energy gained by the ice is equal to the energy lost by the hot tea, assuming no heat is lost to the surroundings.
First, we need to calculate the energy lost by the hot tea. We can use the formula:
Q = m * c * ΔT
Where:
Q is the amount of energy 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
For the hot tea:
m = 0.250 kg (mass of hot tea)
c = 4186 J/kg·°C (specific heat capacity of water)
ΔT = (8.00°C - 99.0 °C) = -91.0 °C
Q(hot tea) = 0.250 kg * 4186 J/kg·°C * -91.0 °C
Next, we need to calculate the energy gained by the ice. We'll use a similar formula to the one above:
For the ice:
m = mass of ice we want to find
c = 2090 J/kg·°C (specific heat capacity of ice)
ΔT = (8.00 °C - 0.00 °C) = 8.00 °C
Q(ice) = m * 2090 J/kg·°C * 8.00 °C
Since energy gained by the ice is equal to the energy lost by the hot tea, we can equate the two equations:
m * 2090 J/kg·°C * 8.00 °C = 0.250 kg * 4186 J/kg·°C * -91.0 °C
Now we can solve for the mass of ice, m:
m = (0.250 kg * 4186 J/kg·°C * -91.0 °C) / (2090 J/kg·°C * 8.00 °C)
By simplifying the equation, we get:
m = -1.125 kg
We can ignore the negative sign since mass can't be negative, so the mass of ice required to reach a final temperature of 8.00 °C is approximately 1.125 kg.
Therefore, Emily must add about 1.125 kg of ice at 0.00 °C to the hot tea to reach a final temperature of 8.00 °C.