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.)
My work:
(0.25)(4186)(91) + m(4186)(-8)(3.35 ×10^5)=0
My answer: 0.316
It says Im wrong...what did i do wrong?
the correct answer is 0.258. you have to do the multiplication for the latent heat of fusion and the Q=mc∆T equations separately and then add the two together because those are your x-values, or your unknowns (the mass in kg). Next, you take the sum of those equations and you divide it by the
Q=mc∆T answer you got with the warm water.
I got same thing idk
To solve this problem correctly, you need to apply the principle of conservation of energy. The principle states that the heat gained by the cold object (ice) equals the heat lost by the hot object (tea), assuming no heat is lost to the surroundings.
Here's the step-by-step solution:
1. Determine the heat lost by the hot tea:
Q_hot = mass_hot * specific heat capacity * (initial temperature_hot - final temperature)
Q_hot = (0.25 kg) * (4186 J/kg°C) * (99.0°C - 8.0°C)
= 8,685 J
2. Determine the heat gained by the ice:
Q_cold = mass_cold * specific heat capacity * (final temperature - initial temperature_cold)
Q_cold = mass_cold * (4186 J/kg°C) * (8.0°C - 0.0°C)
= 33488 J * mass_cold
3. Set the equation equal to each other since heat gained = heat lost:
Q_hot = Q_cold
8,685 J = 33488 J * mass_cold
4. Solve for the mass of ice, "mass_cold":
mass_cold = 8,685 J / 33488 J
mass_cold ≈ 0.259 kg
Therefore, Emily needs to add approximately 0.259 kg of ice to the tea to reach a final temperature of 8.0°C.
To solve this problem, you need to use the principle of conservation of energy. The heat gained or lost by the tea must be equal to the heat gained or lost by the ice.
First, calculate the heat lost by the tea using the formula:
Q = mcΔT
where Q is the heat lost, m is the mass of the tea, c is the specific heat capacity of water, and ΔT is the change in temperature.
Q = (0.250 kg)(4186 J/kg°C)(99.0°C - 8.0°C)
Q = 85,180 J
Next, calculate the heat gained by the ice using the same formula:
Q = mcΔT
where Q is the heat gained, m is the mass of the ice, c is the specific heat capacity of water, and ΔT is the change in temperature.
Q = (m kg)(4186 J/kg°C)(8.0°C - 0.0°C)
Q = 33488 m J
Since the heat lost by the tea must be equal to the heat gained by the ice, you can set up the equation:
85,180 J = 33488 m J
Now, solve for the mass of the ice:
m = (85,180 J) / (33488 J/kg)
m = 2.546 kg
So, Emily must add 2.546 kg of ice to the tea in order to reach a final temperature of 8.0°C.
Your calculation seems to be incorrect. Make sure you are correctly calculating the heat lost by the tea and the heat gained by the ice, and then equating these values to solve for the mass of the ice.