Latent Heat and Clapeyron Equation Manipulation

[Pawnag3]

Hi,
I just want to double check if the following is valid. However, I would just like to give you the context of my questions. Basically, I am passing a wire through ice, then I'm trying to figure out how an increase in mass (therefore force) affects the velocity at which the wire goes through.
First, here are the two formulas that I'm using:
1) Q = mL, where L is the latent heat of fusion of water.
2) Part of the Clausius-Clapeyron relation where:
https://www.physicsforums.com/attachment.php?attachmentid=28794&stc=1&d=1286245341

Then, I combined the two together by subbing in for L, so that:
https://www.physicsforums.com/attachment.php?attachmentid=28797&stc=1&d=1286245421

Then, energy = 1/2 mv^2, therefore, we get:
https://www.physicsforums.com/attachment.php?attachmentid=28798&stc=1&d=1286245490

Is the above remotely correct? Does anyone have any ideas on how I can combine the equations?

Thanks in advance

 

[jbsteele]

!Yes, the above is correct. To combine the equations, you need to rearrange the first equation to solve for m, and then substitute it into the second equation. Doing so, you will get an equation that relates the velocity of the wire with the mass and the temperature of the ice.