A 5.0-gram sample of gold and a 5.0-gram sample of iron both absorb exactly 25 calories of energy. The specific heat of gold is 0.03 cal/g°C. The specific heat of iron is 0.11 cal/g°C. Which of the following statements is true?
A) The gold sample will experience a greater increase in temperature.
B) The iron sample will experience a greater increase in temperature.
C) Both samples will experience the same increase in temperature.
How would i figure this one out?
A. It takes only .03 cal to heat a gram of gold a degree but much more to heat the same mass of iron a degree.
Think about the equation that defines specific heat:
Q = M*C*(delta T)
In your case, Q (the added heat) and M (the mass) are the same for gold and iron.
That means delta-T (the change in termperature) is inversely proportional to C, the specific heat.
delta T = (Q/M)*(1/C)
You should be able to figure it out from there.
So the gold sample will experience a greater increase in temperature?
Yes. Because gold has a lower specific heat (per unit mass), its temperature rises more.
Okay. Thank you for the help (:
Thanks to both of you (:
To determine which statement is true, you need to compare the change in temperature of the gold sample and the iron sample.
The heat gained or lost by a substance can be calculated using the formula:
Q = mcΔT
Where:
Q = Heat gained or lost (in calories)
m = Mass of the substance (in grams)
c = Specific heat of the substance (in cal/g°C)
ΔT = Change in temperature (in °C)
In this case, both the gold and iron samples absorbed 25 calories of energy (Q). We can rearrange the formula to solve for the change in temperature (ΔT):
ΔT = Q / (mc)
Now, let's calculate the change in temperature for each sample.
For gold:
m = 5.0 grams
c = 0.03 cal/g°C
ΔT(gold) = 25 calories / (5.0 grams * 0.03 cal/g°C)
ΔT(gold) = 25 calories / 0.15 cal/°C = 166.67 °C
For iron:
m = 5.0 grams
c = 0.11 cal/g°C
ΔT(iron) = 25 calories / (5.0 grams * 0.11 cal/g°C)
ΔT(iron) = 25 calories / 0.55 cal/°C = 45.45 °C
Comparing the change in temperature for gold and iron:
ΔT(gold) > ΔT(iron)
This means that the gold sample will experience a greater increase in temperature compared to the iron sample. Therefore, the correct statement is:
A) The gold sample will experience a greater increase in temperature.