MHB How Much Heat Is Needed to Melt Ice and Warm It to 30°C?

  • Thread starter Thread starter Fantini
  • Start date Start date
  • Tags Tags
    Change Heat Ice
Fantini
Gold Member
MHB
Messages
267
Reaction score
0
Here's the problem.

How much heat is required to raise the temperature of $50.0$g of H$_2$O ice at $0.00^{\circ}$C to $30.0^{\circ}$C? Assume an average $1.00 \text{ cal/g}^{\circ}$C specific heat for water in this temperature range.

Since he said ice I assumed all $50.0$g is ice and therefore you need to both convert the ice to water than then heat the water. This amounts to

$$Q = mL + mc \Delta T = 50 \cdot 80 + 50 \cdot 1 \cdot 30 = 5500 \text{ cal}.$$

However the book answer is $1500$ cal, which I disagree. This is the amount of heat necessary to heat the water, but not to turn all ice to water.

Am I wrong?
 
Mathematics news on Phys.org
Well, the book is not converting the ice to water, right? If you just do the $m c \Delta T$ bit, you get the book's answer.

I would definitely have approached it the way you did, because I'm not sure I can conceive of a block of ice at $30^{\circ}\text{C}$. I suppose you could prove the book wrong if, in a vacuum (best-case scenario), heating the block of ice to $30^{\circ}\text{C}$ would have to melt it. It is true that the heat required to melt is considerably more than the heat required to raise the temperature. Still, my intuition is strongly on your side.
 
I'm guessing this is just an oversight from the book. He even labeled the exercise as Latent Heat. These things happen. :)
 
Fantini said:
I'm guessing this is just an oversight from the book. He even labeled the exercise as Latent Heat. These things happen. :)

So it looks like an example what would happen if you do not take latent heat into account. (Wink)
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top