# thermodynamics

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Hey guys. Thanks for all the help in the past. I now have another question to solve. Not sure which equation to use or even how to start . Here's the question. Four kg of ice, are mixed with 60 kg of water which is at a temperature of 50 degrees C and the resultant temperature is 40 degree C. Calculate the initial temperature of the ice if its SPECIFIC heat is 2.04 kj/kg K and it LATENT heat is 335 kj/kg. Take the specific heat of water as 4.2 kj/kgK. Thanks again

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The latent heat is how much energy you need to add, per unit mass, to melt the ice at 0 C. The specific heat is the energy required, per unit mass, to change the temperature. You know the final mass and temperature and that energy is conserved.

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Also, I'm moving this to a Physics forum since it's quite out of place in the maths section.

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(delta)Q=m*c*(delta)t + mL

Q=heat, m=mass, c=specific heat, t=time, L=latent heat

Set the two heat differences equal to each other, so it should look like this:

m(water)*c(water)*(delta)t(water)=m(ice)*c(ice)*(delta)t(ice) + m(ice)L(ice)

The (delta)t would then be: t(final)-t(initial), or vice versa depending on which is bigger. t(final) is the same on both sides of the equation. After knowing that, all you have to do is factor and do the algebra.

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