A 100 kg sample of a metal is cooled from 100°C to 20°C by removing 20 kcal of heat. Calculate the specific heat capacity of the metal.
Why did the metal go to therapy? Because it had too many issues with its specific heat capacity! But don't worry, I'm here to help. Let's get serious for a moment and do some math.
The specific heat capacity (C) of a substance is the amount of heat energy (Q) required to change the temperature of 1 gram of the substance by 1 degree Celsius (or Kelvin). In this case, we have a 100 kg sample of the metal, so we need to convert that to grams by multiplying by 1000.
Q = 20 kcal = 20,000 calories (since 1 kcal = 1000 calories)
m = 100 kg = 100,000 grams
ΔT = (Tf - Ti) = (20°C - 100°C) = -80°C
Now, we can use the formula Q = m * C * ΔT to solve for C.
20,000 calories = 100,000 grams * C * -80°C
C = -20,000 calories / (100,000 grams * -80°C)
C = 0.025 calories/(gram °C)
So, the specific heat capacity of the metal is 0.025 calories per gram per degree Celsius. But remember, this is assuming the metal is not a clown-shaped metal! *wink*
To calculate the specific heat capacity of a substance, we can use the formula:
Q = m * c * ΔT
Where:
Q is the heat transferred
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
In this case, we know:
Q = -20 kcal (negative because heat is removed)
m = 100 kg
ΔT = 100°C - 20°C = 80°C
Substituting the known values into the formula, we have:
-20 kcal = 100 kg * c * 80°C
To convert kcal to joules, we can use the conversion factor:
1 kcal = 4184 J
Therefore, -20 kcal = -20 * 4184 = -83680 J.
-83680 J = 100 kg * c * 80°C
Rearranging the equation to solve for c, we get:
c = -83680 J / (100 kg * 80°C)
Evaluating this equation, we find:
c ≈ -0.104 J / (kg°C)
So, the specific heat capacity of the metal is approximately -0.104 J / (kg°C). Note that the negative sign indicates that heat is removed as the metal cools down.
To calculate the specific heat capacity of the metal, we can use the formula:
Q = m * c * ΔT
Where:
Q is the heat energy transferred (in calories or kcal),
m is the mass of the metal (in grams or kg),
c is the specific heat capacity of the metal (in cal/g°C or kcal/kg°C), and
ΔT is the change in temperature (in °C).
Given information:
m = 100 kg (mass of metal)
ΔT = 100°C - 20°C = 80°C (change in temperature)
Q = 20 kcal (heat energy transferred)
Rearranging the formula, we have:
c = Q / (m * ΔT)
Now, let's substitute the given values and calculate the specific heat capacity:
c = 20 kcal / (100 kg * 80°C)
c = 0.025 kcal/kg°C
Therefore, the specific heat capacity of the metal is 0.025 kcal/kg°C.