A metal is thought to be copper or gold. When 18 g of the metal absorbs 58 cal, its temperature rises by 35 °C.
a. What is the specific heat, in cal/g °C, of the metal?
b. Would you identify the metal as copper or gold?
The table we were given says:
Copper, Cu(s) : .0920 cal/g °C
Gold, Au(s) : .0308 cal/g °C
q = mass metal x specific heat metal x delta T
58 = 18 g x specific heat x 35
58/(18*35) = ?
What do you think it is?
Thank you so much!
58/18 * 35 = 0.0920, which is copper.
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a. Well, let's crunch some numbers and find out! To determine the specific heat, we can use the equation:
Q = mcΔT
Where Q is the heat absorbed (58 cal), m is the mass of the metal (18 g), c is the specific heat, and ΔT is the change in temperature (35 °C).
Plugging in our values, we can solve for c:
58 cal = (18 g) * c * 35 °C
Simplifying the equation:
58 = 630c
Dividing both sides by 630:
c ≈ 0.0921 cal/g °C
So the specific heat of the metal is approximately 0.0921 cal/g °C.
b. Now it's time for the big reveal! Comparing the specific heat we found (0.0921 cal/g °C) to the specific heats given in the table, it matches perfectly with copper!
Therefore, we can confidently identify the metal as copper. Woohoo! Copper for the win! 🎉
To find the specific heat of the metal, we can use the formula:
\( q = mcΔT \)
where:
q is the heat absorbed by the metal (in calories)
m is the mass of the metal (in grams)
c is the specific heat of the metal (in cal/g °C)
ΔT is the change in temperature of the metal (in °C)
In this case, we're given:
q = 58 cal
m = 18 g
ΔT = 35 °C
Plugging in these values into the formula, we have:
\( 58 = 18c35 \)
To solve for c, we can divide both sides of the equation by \( 18 \times 35 \):
\( \frac{58}{18 \times 35} = c \)
Calculating the value gives us:
\( c \approx 0.0910 \) cal/g °C
So, the specific heat of the metal is approximately 0.0910 cal/g °C.
To identify the metal as copper or gold, we can compare the calculated specific heat with the specific heats given in the table.
The specific heat of copper (Cu) is 0.0920 cal/g°C, which is very close to the calculated specific heat. On the other hand, the specific heat of gold (Au) is 0.0308 cal/g°C, which is significantly different from the calculated specific heat.
Therefore, we can conclude that the metal is most likely copper (Cu).