What equations are needed and how do I solve for these?

Question

a) A 0.400 kg sample of aluminum (c = 9.10 x 10² J/kg°C) at 95°C is dropped into a

0.550 kg pot of water which is at 18°C. What temperature will the mixture come to?

b) How much thermal energy is absorbed by a 0.0220 kg ice cube as it melts? For

this problem, let the latent heat of fusion in water be 3.4 x 10⁵ J/kg.

Answer 1

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.

m_waterC_waterΔT_water = m_AlC_AlΔT_Al (Assuming C_water = 4184 J/KgC)

Next, you will solve for one of the ΔT's in terms of the other. If we use ΔT_water then we get

ΔT_water = ΔT_Al (_AlC_A/m_waterC_water) which upon plugging in the numbers is 0.158ΔT_Al

Now you will set up an equation to determine at what ΔT_Al the two temperatures are the same:

95 C - ΔT_Al = 18 C + 0.158ΔT_Al ; solving you get ΔT_Al = 66.5 C

Thus, using ΔT_Al 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.