Question

The specific heats of some elements at 25°C are as follows: aluminum = 0.215 cal/g⋅°C; carbon (graphite) = 0.170 cal/g⋅°C; iron = 0.107 cal/g⋅°C; mercury = 0.0331 cal/g⋅°C.
1- Which element would require the smallest amount of heat to raise the temperature of 100. g of the element by 10.°C?
2- If the same amount of heat needed to raise the temperature of 1 g of aluminum by 59°C were applied to 1 g of mercury, by how many degrees would its temperature be raised?
3- If a certain amount of heat is used to raise the temperature of 1.6 g of iron by 10.°C, the temperature of 1 g of which element would also be raised by 10.°C, using the same amount of heat?

Answer 1

Answer:304 cal

 

Explanation:

The specific heat of aluminium tells you the amount of energy needed to increase the temperature of  

1 g

of aluminium by  

1

∘

C

.

c

Al

=

0.214 cal g

−

1

∘

C

−

1

You can thus say that in order to increase the temperature of  

1 g

of aluminium by  

1

∘

C

, you need to supply it with  

0.214 cal

of heat.

Now, you know that your sample has a mass of  

55.5 g

. Use the specific heat of aluminium to calculate how much heat would be needed to increase the temperature of this sample

55.5

g

⋅

0.214 cal

1

g

⋅

1

∘

C

=

11.877 cal

∘

C

−

1

So, you now know that in order to increase the temperature of  

5.5 g

of aluminium by  

1

∘

C

, you need to supply it with  

11.877 cal

of heat.

But since you know that the temperature change is equal to

48.6

∘

C

−

23.0

∘

C

=

25.6

∘

C

you can say that you will need

25.6

∘

C

⋅

for 55.5 g of Al



11.877 cal

1

∘

C

=

304 cal

−−−−−−  

The answer is rounded to three sig figs.

Explanation: