Specific heat capacity of a solid material

[Aleisha]

Homework Statement

A 4.80 kg piece of solid material is heated from 16.4C to 219C (3 s.f.) using 787 kJ of energy (3 s.f.).

Assuming an efficiency of 0.383 for the heating process, and that the material does not melt, calculate the specific heat capacity of the material.

Homework Equations

Q=mc(Change in T)

The Attempt at a Solution

c=Q/ m (Delta T)
=(787e3)/ (4.80 x 202.6)
= 809.2711418 k/kg/K
However they have given me a efficiency of 0.383? Do i just time that by my answer? We haven't been taught about efficiency.

Thank you

 

[haruspex]

We haven't been taught about efficiency.

If you use 1kJ of energy in a heating process, but the process is only 30% efficient, how much heat ends up where it is wanted? (Not something that really requires teaching, I'd say.)

 

[Dr Dr news]

Your methodology is correct as is your answer if all of the heat energy goes into heating the body. If however, only 38.37% of the heat energy supplied goes into heating the body, you need to make an adjustment in your calculation.

 

[Aleisha]

If you use 1kJ of energy in a heating process, but the process is only 30% efficient, how much heat ends up where it is wanted? (Not something that really requires teaching, I'd say.)

So my answer will be approximately 30% of 809.27k/kg/K?

 

[Aleisha]

Your methodology is correct as is your answer if all of the heat energy goes into heating the body. If however, only 38.37% of the heat energy supplied goes into heating the body, you need to make an adjustment in your calculation.

Thank you very much! So I should just find 38.3% of my answer (809.27)? Is that correct because it’s only being 30% efficient in its absorbance?

 

[haruspex]

So my answer will be approximately 30% of 809.27k/kg/K?

That's the approach, but not 30%. That was a number I made up to illustrate. Use the given 0.383, i.e. 38.3%.

 

[Aleisha]

That's the approach, but not 30%. That was a number I made up to illustrate. Use the given 0.383, i.e. 38.3%.

Yes that’s understandable thank you :)

 

[haruspex]

Yes that’s understandable thank you :)

There's another thread currently that looks the exact same problem, just slightly different numbers. I guess this is software generated. We can't find an error in the student's work (unless wrong numbers were posted in the thread), but the software is rejecting the answer.
I'd be interested to know whether you have better luck.

 

[Aleisha]

There's another thread currently that looks the exact same problem, just slightly different numbers. I guess this is software generated. We can't find an error in the student's work (unless wrong numbers were posted in the thread), but the software is rejecting the answer.
I'd be interested to know whether you have better luck.

I got an overall answer of 310 J/kg/K and the answer was correct. All the data was copy and pasted from my question. Thank you for your help :)

 

[haruspex]

I got an overall answer of 310 J/kg/K and the answer was correct. All the data was copy and pasted from my question. Thank you for your help :)

OK, thanks