Question

When the same amount of heat is added to 50.0 g of each substance, which of the following will have the greatest temperature increase?

iron

gold

aluminum

copper

Answer 1

here is the chart they gave me
Substance C[ J/g.C∘ ]
iron 0.46
aluminum 0.90
gold 0.13
copper 0.39

Answer 2

aluminum ? i think or gold?

Answer 3

Sorry, I worded it wrong. Let me rephrase.

Answer 4

its okay(:

Answer 5

The formula for heat energy is

\(q=mC_s∆T\)
where \(q\) is theat transferred
\(m\) is mass in grams
\(C_s\) is specific heat capacity
and
\(∆T\) is change in temperature.


The question indicates that the amount of heat added \(q\) and the mass \(m\)=50g is constant. It is asking which substance, according to it's specific heat capacity, will have the greatest change in temperature \(∆T\)

To make things more understandable, I will assign an arbitrary magnitude for the heat added \(q\) as \(q=100 J\). This is certainly not realistic but it will help us throughout

Hence

\(100~J=(50.0~g)(C_s)(∆T)\)
\(2=C_s∆T\)

Moving along with the question, we are asked to find which metal will have the greatest ∆T. To have the greatest ∆T, we should have the lowest \(C_s\), correct? This proves us that
\(C_s~\frac{1}{∝} ∆T\)

In order to have the greatest ∆T in these conditions, we need the metal with the lowest \(C_s\)

Hence, the substance with the lowest specific heat capacity should yield your answer.

Answer 6

This would then indeed be gold since from the table it is the lowest! this makes sense, much easier than i originally thought. i truly appreciate your explanation, im going to take a screenshot of this a write notes on it ! this is great information, thanks again.

Answer 7

np a pleasure (:

Answer 8

looking back on this one, im actually not sure if it gold? was i correct because instn spcefic heat cpacity in terms of J g^-1 K^-1 , but the table they gabe me was in terms of C[ J/g.C∘ ] , i dont know the difference between them ? are they the same

Answer 9

because isnt*

Answer 10

gave*

Answer 11

I understand your question, and yes, they are slightly separate units. However, we do not actually need to worry about the other unit, because the point of the question was to see the relation between \(C_s\) and \(∆T\), and hence it is gold.

But anyway, I'll go over this too.
It just means that using the values of \(C_s\) in \(J~g^{-1}~°C^{-1}\), we can calculate for it in \(J~g^{-1}~K^{-1}\). They are proportional, so there is no difference in our answer.

It is helpful to know the variations between the three main temperature scales used in Chemistry:
\(K\) is a ratio temperature scale. \(°C\) and \(°F\) are changed at a interval scale. You'll probably understand this more if you take statistics, but that means that if K=0, that means that there is NO K. If C or F are 0, that means that there is some magnitude out of an interval.

Answer 12

ohhh okay this makes sense! thank you for explaining that,i will l take note of this(: