Specific Heat Capacity Question - Unknown Mass

In summary, the thermal energy is supplied to a melting solid at a constant rate of 2000 W and it melts in 2.0 minutes to produce a mass of 2.5 kg.
  • #1
me240
5
0
Q. Thermal energy is supplied to a melting solid at a constant rate of 2000 W. Calculate the mass of the solid changed to liquid in 2.0 minutes. Assume that the specific latent heat of fusion of the solid is 95 000 J kg-1 and that heat exchange with the surroundings may be neglected.

I was doing my physics homework just fine until I came to this question. I have NO idea how to do this :s Please help!

Note: I'm really bad physics. Like REALLY bad and I've just started to get the hang of it a little.
 
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  • #2
What is the total heat energy supplied to the melting solid over the time interval?
 
  • #3
I believe it'll be 2000 W x 2.0 minutes = 4000 J
Do I need to convert it into seconds first?
 
  • #4
me240 said:
I believe it'll be 2000 W x 2.0 minutes = 4000 J
Do I need to convert it into seconds first?
Yes, you do need to convert it into seconds because one watt of power is equivalent to one joule of energy input/output per second. W = J/s
 
  • #5
Right.
So 2 minutes = 120 s
2000 x 120 = 240000 J

How do I find the mass now?
 
  • #6
Good, so we've established that 240 kJ of thermal energy was supplied to melt the solid. From your inability to carry on, I gather that you have no idea what the "specific latent heat of fusion" means? The specific latent heat of fusion of a substance is defined as the energy per unit mass required to change the substance from the solid to liquid phase (ie melt it) without any change in temperature. In this case, this implies that 95 kJ of energy is required to just melt 1 kg of the solid. So, if we had to use 240 kJ of energy to melt the amount of solid that we have, how many kilograms would that be?
 
  • #7
That makes a lot more sense now :)
240 ÷ 95 = 2.526315789
Not quite sure how to round this...
 
  • #8
The convention is to round it so that it has the same number of significant digits as the least accurate input number. Here, you can just round to 2.5, because 95 has two significant digits.
 
  • #9
Thank you so much both of you. This was really helpful for such a non-physics person like me.
God bless you two!
 

FAQ: Specific Heat Capacity Question - Unknown Mass

1. What is specific heat capacity?

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It is often denoted by the symbol "C" and is measured in units of joules per gram per degree Celsius (J/g°C).

2. How is specific heat capacity different from heat capacity?

Specific heat capacity is a measure of the amount of heat required to raise the temperature of a specific quantity (usually one gram) of a substance, while heat capacity is a measure of the amount of heat required to raise the temperature of the entire mass of a substance. In other words, specific heat capacity takes into account the mass of the substance, while heat capacity does not.

3. How do you calculate specific heat capacity?

Specific heat capacity can be calculated by dividing the amount of heat (in joules) transferred to a substance by the product of its mass (in grams) and the change in temperature (in degrees Celsius).

4. Why is it important to know the specific heat capacity of a substance?

Knowing the specific heat capacity of a substance is important in understanding how it will behave when heated or cooled. It can also be used in various calculations, such as determining the amount of energy needed to heat a substance to a certain temperature.

5. How can the specific heat capacity of an unknown substance be determined?

The specific heat capacity of an unknown substance can be determined through experimentation. This involves measuring the amount of heat required to raise the temperature of a known mass of the substance by a certain amount. By rearranging the equation for specific heat capacity, the value of C can be calculated and used to identify the substance.

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