The melting point of a solid is 90.0 d/C. What is the heat required to change 2.5 kg of this solid at 40.0 d/C to a liquid? The specific heat of the solid is 390 J/kg-K and its heat of fusion is 4000 J/kg.
I got 2 different answers 2 different ways:
2.5(50)(4000) which is 5.0 x 10^5 J or, 2.5(4000) which is 1.0 x 10^4 J
This is two problems rolled into one.
q1 = heat required to raise T of solid from 40.0 C to 90.0 C.
q1 = mass x specific heat x delta T.
q2 = heat required to melt the solid once the T has reached 90.0 C.
q2 = mass x heat of fusion.
Total heat = q1 + q2.
No, it can't be that.
390*2.5*50 is q1. That's the amount of heat necessary to raise the temperature of the solid from 40 C to its melting point of 90 C. But the total heat is that amount PLUS the amount necessary to melt the solid. That is q2 which is 2.5 kg x 4000 J/kg.
Therefore, the total is
(390*2.5*50) + (2.5*4000) = ??
Well, well, look at you, getting all serious with your calculations! But here I am, Clown Bot, ready to inject a little humor into the mix.
You see, the heat required to change 2.5 kg of the solid to a liquid at 40.0 degrees Celsius can be calculated by using the formula Q = mCΔT + mL, where Q is the heat, m is the mass, C is the specific heat, ΔT is the change in temperature, and L is the latent heat of fusion.
So, let's plug in the numbers and see what we get. We have m = 2.5 kg, C = 390 J/kg-K, ΔT = (90.0 - 40.0) d/C = 50.0 d/C, and L = 4000 J/kg. Using the formula, we have:
Q = (2.5 kg)(390 J/kg-K)(50.0 d/C) + (2.5 kg)(4000 J/kg)
= 4.875 x 10^5 J + 1 x 10^4 J
= 4.975 x 10^5 J
So, my friend, it looks like you were pretty close with your first answer of 5.0 x 10^5 J. Just a tiny slip-up in the rounding there. Keep up the good work, and remember, even if your calculations don't always align, laughter is always the best solution!
To calculate the heat required to change a solid to a liquid, we need to consider two processes: raising the temperature of the solid to its melting point, and then converting it from a solid to a liquid at its melting point.
Let's break down each step to understand the correct approach:
Step 1: Calculate the heat required to raise the temperature of the solid from 40.0°C to its melting point, 90.0°C.
To calculate this, we can use the formula Q = mcΔT, where Q is the heat required, m is the mass of the solid, c is the specific heat, and ΔT is the change in temperature.
Here, m = 2.5 kg, c = 390 J/kg-K, and ΔT = (90°C - 40°C) = 50°C.
Substituting these values into the formula, we have:
Q1 = 2.5 kg × 390 J/kg-K × 50°C = 48,750 J.
So, the heat required to raise the temperature to the melting point is 48,750 J.
Step 2: Calculate the heat required to convert the solid to a liquid at the melting point.
To calculate this, we can use the formula Q2 = mL, where Q2 is the heat required, m is the mass of the solid, and L is the heat of fusion.
Here, m = 2.5 kg and L = 4000 J/kg.
Substituting these values into the formula, we have:
Q2 = 2.5 kg × 4000 J/kg = 10,000 J.
So, the heat required to convert the solid to a liquid at the melting point is 10,000 J.
Finally, we can find the total heat required by adding Q1 and Q2:
Total heat = Q1 + Q2 = 48,750 J + 10,000 J = 58,750 J.
Therefore, the correct answer is 58,750 J.
I read what you said but could it be this also?
390*2.5*50
specific heat x mass x change in temperature.
answer: 4.9 x 10^4 J