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Old Nov 24th 2017, 09:28 AM   #1
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Latent Heat

One more question-

How much heat is required to change 1.83 kg of solid lead at 135C to liquid lead at 327C?

I'm assuming I have to use both the equations, Q=cm△T and Q=Lf*m.
I wasn't sure how to go about it so I solved Q=Lf*m and got 4.28e4, then used it for Q=4.28e4(192) and got 8.2e6 but the answer says its 8.74e4, and I haven't been able to redo it successfully. Am I doing any of it right?
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Old Nov 24th 2017, 10:24 AM   #2
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The equation for sensible heat exchange ($\displaystyle Q = mc \Delta T$) is used when a substance is changing its temperature, but not its phase.

The equation for latent heat exchange ($\displaystyle Q = mL$) is used when a substance is changing its phase, but not its temperature.

You should not use one heat term with the other... they are different processes and the equations need to be kept separate. However, you can add up the individual results to get the total heat transfer if both processes occur.

Therefore, the total amount of heat transfer to change its temperature from 135 degrees Celsius to 327 degrees Celsius and turn it from a solid to a liquid is

$\displaystyle Q_{total} = Q_{sens} + Q_{lat}$
$\displaystyle = m c \Delta T + mL$
$\displaystyle = 1.83 \times 128 (327 - 135) + 1.83 \times 22400$
$\displaystyle = 44974 + 40992$
$\displaystyle = 85966 J$

The discrepancy between this answer and the answer you stated (8.74e4) is probably due to the choice of heat capacity, c, and latent heat of melting, L. I chose

$\displaystyle c = 128 J kg^{-1} K^{-1}$
$\displaystyle L = 22.4 kJ kg^{-1} = 22400 J kg^{-1}$

which I pulled from the website "Engineering toolbox". If the problem comes with particular choices of c and L, you should use those instead.
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Old Nov 28th 2017, 06:10 AM   #3
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Originally Posted by benit13 View Post
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The equation for sensible heat exchange ($\displaystyle Q = mc \Delta T$) is used when a substance is changing its temperature, but not its phase.

The equation for latent heat exchange ($\displaystyle Q = mL$) is used when a substance is changing its phase, but not its temperature.

You should not use one heat term with the other... they are different processes and the equations need to be kept separate. However, you can add up the individual results to get the total heat transfer if both processes occur.

Therefore, the total amount of heat transfer to change its temperature from 135 degrees Celsius to 327 degrees Celsius and turn it from a solid to a liquid is

$\displaystyle Q_{total} = Q_{sens} + Q_{lat}$
$\displaystyle = m c \Delta T + mL$
$\displaystyle = 1.83 \times 128 (327 - 135) + 1.83 \times 22400$
$\displaystyle = 44974 + 40992$
$\displaystyle = 85966 J$

The discrepancy between this answer and the answer you stated (8.74e4) is probably due to the choice of heat capacity, c, and latent heat of melting, L. I chose

$\displaystyle c = 128 J kg^{-1} K^{-1}$
$\displaystyle L = 22.4 kJ kg^{-1} = 22400 J kg^{-1}$

which I pulled from the website "Engineering toolbox". If the problem comes with particular choices of c and L, you should use those instead.

Thank you!!
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