Calculating Time to Melt Substance at 80 C

[lalala_land89]

a portion of an electirc circuit connected toa 40-ohm resistor is embedded in .2 kg of a solid substance in a calorimeter. The externam portion of the circuit is connected to a 60 V power supply.

At 80 C the substance begins to melt. The heat of fusion of the substance is 1.35*10^5 J/kg. How long after the temperature reaches 80 C will it take to melt all of the substance?

I really don't understand how to find time. I get that there's a way to find heat of fusion, but it's already given to me. help please

i have originally posted this in the advanced physics but no one helped. maybe someone here will.

 

[Gyroscope]

What is the energy delivered per second to the substance?

Can you find the power of the power supply? (Hint: P=UI and Ohm's Law)

 

[m2003]

I understand your confusion and I am happy to help you with this problem. To calculate the time it takes for the substance to melt at 80 C, we need to use the equation Q = mCΔT, where Q is the heat energy, m is the mass of the substance, C is the specific heat capacity, and ΔT is the change in temperature.

In this case, we know the heat of fusion (1.35*10^5 J/kg) and the mass of the substance (0.2 kg), but we need to find the specific heat capacity. The specific heat capacity is the amount of heat energy required to raise the temperature of 1 kg of a substance by 1 degree Celsius. Since the substance is already at 80 C, we can assume that it has reached its melting point and its specific heat capacity is now the heat of fusion. Therefore, we can substitute 1.35*10^5 J/kg as the specific heat capacity in the equation.

Next, we need to find the total heat energy required to melt the substance. This can be calculated by multiplying the heat of fusion by the mass of the substance, which gives us 1.35*10^5 J.

Now, we can rearrange the equation to solve for time (t): t = Q / (mCΔT). Plugging in the values, we get t = (1.35*10^5 J) / (0.2 kg * 1.35*10^5 J/kg * 80 C) = 1 second.

Therefore, it will take 1 second for the substance to melt completely at 80 C. I hope this helps you understand how to calculate the time it takes for a substance to melt. If you have any further questions, please don't hesitate to ask.