Elias K. answered • 05/16/24
Tutor for Chemistry, Physics, Biology, and Calculus
You will need the Heat Energy Equation Q = mCT where m is the mass of the substance, C is the specific heat capacity, and T is the temperature change. This equation tells you how much heat a substance absorbs/releases for a given temperature change. To solve this problem, you will need to determine for what temperature changes the amount of heat absorbed by the water is equal to the heat released by the aluminum. Therefore you will set the Heat Energy equations for each of these substances equal.
mwaterCwaterΔTwater = mAlCAlΔTAl (Assuming Cwater = 4184 J/KgC)
Next, you will solve for one of the ΔT's in terms of the other. If we use ΔTwater then we get
ΔTwater = ΔTAl (AlCA/mwaterCwater) which upon plugging in the numbers is 0.158ΔTAl
Now you will set up an equation to determine at what ΔTAl the two temperatures are the same:
95 C - ΔTAl = 18 C + 0.158ΔTAl ; solving you get ΔTAl = 66.5 C
Thus, using ΔTAl you can determine that the final temperature is 28.5 C
For part b, a much simpler process is required as you are given a Heat of Fusion which does not factor in temperature changes due to all phase changes occurring at constant temperature. Therefore, to determine the heat absorbed you simply multiply the mass of the ice by its heat of fusion.
AK K.
Sorry about the formatting of the message. Hitting 'Enter' doesn't seem to keep the spacing between paragraphs but I hope what I noted makes sense :)05/27/24
AK K.
I also did find that the second question was very easy to solve. I used the formula Q = m x L where Q = thermal energy absorbed in joules, m = mass of ice cube in kg, and L = latent heat of fusion in J/kg Since m and L were given, I substituted those values into the equation which gave me Q = 7480 Joules Do you think this is correct?05/27/24
AK K.
Hi! Sorry for getting to this late, I did not find any notifications to this...... I answered the question from earlier, and I got a variety of different results (many because of my own mistakes) but one recurring one was 3.47 C, which I got after using this method: 'Heat lost by aluminum using the equation: Q_lost = m_aluminum x c_aluminum x ΔT_aluminum' where m_aluminum = mass of aluminum = 0.400 kg, c_aluminum = specific heat capacity of aluminum = 9.10 x 10^2 J/kg°C, and ΔT_aluminum = change in temperature of aluminum = (final temperature - initial temperature of aluminum)...... And heat gained by water using the equation: Q_gained = m_water x c_water x ΔT_water where m_water = mass of water = 0.550 kg, c_water = specific heat capacity of water = 4186 J/kg°C, and ΔT_water = change in temperature of water = (final temperature - initial temperature of water) I then set the equations to equal against one another and substituted the values which finally gave me a T_final of 3.47 C. Can you let me know if I approached this correctly?05/27/24