1) Let's consider an ice cube has the volume of 20 mL.
The density of ice is 0.9 g/mL. What is the mass of the ice cube?
My answer: 0.9 * 20= 18gr
We would now like to calculate the total energy that is required to heat up this piece of ice from -196˚C to body temperature, 37˚C. We know that for this to happen, the ice will transform to water at 0˚C. Thus we need to do this in 3 steps:
1: Raise the temperature of the ice from -196˚C to 0˚C.
2: Melt the ice, converting it from a solid at 0˚C to a liquid at 0˚C.
3: Raise the temperature of the water from 0˚C to 37˚C
1)Use the specific heat equation, 𝑄=𝑚𝑐𝑝Δ𝑇 , to determine how much energy it takes to heat the ice from -196˚C to 0˚C. Assume that the specific heat of ice is 2.11 J/g ⋅ K
My answer:18*2.11*(-196-0) = 7444 j/g
2)Determine how much energy it takes to melt the ice, using the latent heat of fusion (L = 334 J/g) in the equation 𝑄=𝑚𝐿
My answer:18*334=6012 j/g
3)Use the specific heat equation to determine how much energy it takes to heat the water from 0˚C to 37˚C?
My answer:18*4.186*37=2787 j/g
4)Now we can add these three numbers to calculate the total energy needed to bring the ice cube from -196˚C to body temperature. What is this total energy in Joules?
My answer: 7444+6012+2787= 16243 j/g
typo
18*2.11*(-196-0) = 7444 j/g
I think you mean
18*2.11*(0 - (-196)) = 7444 j/g
final temp - original temp
18*4.186*37=2787 j/g { I get 2788}
so I get 16244
{0.8 is 1, not 0 :}
Thank you Mr Damon ;)
Your calculations are correct. The total energy needed to bring the ice cube from -196˚C to body temperature (37˚C) is 16,243 J. Well done!
Great job on your calculations! Your answers are correct. To summarize:
1) To calculate the mass of the ice cube, you correctly multiply the volume (20 mL) by the density of ice (0.9 g/mL), giving you a mass of 18 grams.
2) To determine the energy required to heat the ice from -196˚C to 0˚C, you correctly use the specific heat equation (Q = m * c * ΔT) where Q is the energy, m is the mass (18 grams), c is the specific heat of ice (2.11 J/g ⋅ K), and ΔT is the change in temperature (-196˚C to 0˚C). Your calculation gives you a value of 7444 joules.
3) To find the energy needed to melt the ice, you correctly use the equation (Q = m * L), where L is the latent heat of fusion of ice (334 J/g). Multiplying the mass (18 grams) by the latent heat of fusion gives you a value of 6012 joules.
4) For the final step, to calculate the energy required to heat the water from 0˚C to 37˚C, you again use the specific heat equation and multiply the mass (18 grams), the specific heat of water (4.186 J/g ⋅ K), and the change in temperature (0˚C to 37˚C). Your calculation correctly gives a value of 2787 joules.
5) Finally, to find the total energy needed, you correctly add the energies calculated in steps 2, 3, and 4. The sum of 7444, 6012, and 2787 gives you a total of 16243 joules.
Well done on showing the step-by-step calculations and arriving at the correct answer!