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.
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what is it you do not understand. I worked it in one system of units, Professor Elena worked it in another.
Well, well, well, let's see here! So we have a metal sample that's cooling down from 100°C to 20°C by removing 20 kcal of heat? That's quite a cool situation we've got!
Now, to calculate the specific heat capacity, we need to divide the amount of heat removed by the mass of the metal and the change in temperature. In this case, the heat removed is 20 kcal, the mass is 100 kg, and the change in temperature is 100°C - 20°C = 80°C.
Alright, let's get crunching some numbers, my friend! Divide 20 kcal by (100 kg * 80°C), and you'll find that the specific heat capacity of the metal is 0.025 kcal/kg°C.
So, there you have it! The specific heat capacity of the metal is quite a cool 0.025 kcal/kg°C. Keep it chill, my friend!
To calculate the specific heat capacity of the metal, we can use the equation:
Q = mcΔT
Where:
Q is the amount of heat transferred,
m is the mass of the metal,
c is the specific heat capacity of the metal, and
ΔT is the change in temperature.
Given:
m = 100 kg
ΔT = 100°C - 20°C = 80°C
Q = 20 kcal = 20,000 cal (since 1 kcal = 1,000 cal)
Plugging in the values into the equation, we get:
20,000 cal = (100 kg)(c)(80°C)
Dividing both sides by (100 kg)(80°C), we find:
c = 20,000 cal / (100 kg)(80°C)
Simplifying the equation, we get:
c = 2.5 cal / (kg°C)
Therefore, the specific heat capacity of the metal is 2.5 cal/(kg°C).
To calculate the specific heat capacity of the metal, we can use the formula:
Q = mcΔT
Where:
Q is the heat transferred
m is the mass of the metal
c is the specific heat capacity of the metal
ΔT is the change in temperature
Given:
m = 100 kg (mass of the metal)
ΔT = 100°C - 20°C = 80°C (change in temperature)
Q = 20 kcal = 20,000 calories (heat transferred)
Rearranging the formula, we can solve for c:
c = Q / (mΔT)
Plugging in the values, we get:
c = 20,000 calories / (100 kg * 80°C)
c = 250 calories / (kg°C)
Therefore, the specific heat capacity of the metal is 250 calories per kilogram per degree Celsius (cal/(kg°C)).