A 55.0-g piece of copper wire is heated, and the temperature of the wire changes from 19 degrees C to 86 degrees C. The amount of heat absorbed is 343 cal. What is the specific heat of copper?
To find the specific heat of copper, we can use the formula:
q = mcΔT
where:
q is the heat absorbed (343 cal),
m is the mass of the copper wire (55.0 g),
c is the specific heat of copper (to be determined),
and ΔT is the change in temperature (86 degrees C - 19 degrees C = 67 degrees C).
Substituting the given values into the equation, we can solve for c:
343 cal = (55.0 g) × c × 67 degrees C
Now, we can rearrange the equation to isolate c:
c = 343 cal / (55.0 g × 67 degrees C)
Calculating this expression will give us the specific heat of copper.
To find the specific heat of copper, we can use the formula:
Q = mcΔT
Where:
Q = amount of heat absorbed or released (in calories)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in cal/g°C)
ΔT = change in temperature (in °C)
In this case, we are given:
Q = 343 cal
m = 55.0 g
ΔT = (86°C - 19°C) = 67°C
We can rearrange the formula to solve for specific heat (c):
c = Q / (m * ΔT)
Plugging in the values:
c = 343 cal / (55.0 g * 67°C)
Now, let's calculate it step by step:
c = 343 cal / (3,685 g°C)
c = 0.093 cal/g°C
Therefore, the specific heat of copper is approximately 0.093 cal/g°C.