Doubling the Thermal Energy of a Frozen Chocolate Bar

[lxhull]

Homework Statement

Good chocolate is designed to melt at 34 °C. A chocolate bar, initially frozen to a temperature of -115°C, has its thermal energy doubled. Will it melt? Use physics to explain your answer.

Relevant Equations

Eth= mc(change in T)

Eth= thermal energy
M=mass
C= specific heat capacity
T= temperature in celcius

The farthest I got was double thermal energy equals mass times specific heat capacity times change in temperature (115+34)
2Eth=(mc149)
To
Eth=mc74.5
I'm not sure where to go from here. It seems like I don't have enough information.

 

[haruspex]

2Eth=(mc149)

Please define these variables. We should not have to guess their meanings, and we could guess wrongly.
Then explain in words the reasoning behind the equation l

 

[lxhull]

Please define these variables. We should not have to guess their meanings, and we could guess wrongly.
Then explain in words the reasoning behind the equation l

I have done so. Sorry for the confusion, I haven't done this before and forgot.

 

[haruspex]

I have done so. Sorry for the confusion, I haven't done this before and forgot.

Which thermal energy? What it started with or what it had when it reached melting point? Or the difference between them?

 

[Steve4Physics]

The farthest I got was double thermal energy equals mass times specific heat capacity times change in temperature (115+34)

No. Increasing the temperature by (115+34)ºC could less- than-double or more-than-double the thermal energy. You have no way of telling.

Presumably you have stated the question completely and accurately.

When you get a poor/unclear question (which this is), one approach is to make/state some assumption(s) which then allows you to answer.

For example, you could start your answer by saying:
“Assume that the thermal energy of the solid chocolate is proportional to its absolute temperature.”

I’m guessing that’s what whoever wrote the question had in mind. In which case they were wrong – the question is based on incorrect physics!

The above assumption is correct for a fixed amount of ideal gas but not for a solid.

The assumption is equivalent to saying that the ‘c’ in ‘mcΔT’ is a constant - independent of temperature. It isn’t over large temperature ranges.

But with this incorrect assumption, the thermal energy at -115ºC is the amount of energy needed to raise the chocolate from absolute zero (no thermal energy) to -115ºC.

If you are familiar with ‘absolute zero’ and the absolute (kelvin) temperature scale, you should be able to complete the problem using the assumption.

 

[haruspex]

2Eth=(mc149)

If you have x=$100 and you are given another $100, is the amount you have now, y, given by 2y=$100?