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.
To calculate the specific heat capacity of the metal, we need to use the formula:
q = mcΔT
Where:
q = heat energy absorbed or released
m = mass of the metal
c = specific heat capacity of the metal
ΔT = change in temperature
In this case, we know the following values:
m = 100 kg
ΔT = 100°C - 20°C = 80°C
q = 20 kcal
Now, we need to convert the given values to the SI unit system (Joules and Kelvin) because the specific heat capacity is typically measured in Joules per kilogram per Kelvin (J/kg·K).
1 kcal = 4.184 kJ
1°C = 1 K
So, we can convert q to Joules by multiplying it by 4.184:
q = 20 kcal * 4.184 kJ/kcal = 83.68 kJ (or 83,680 J)
Now we can rearrange the formula to solve for c:
c = q / (m * ΔT)
Plugging in the known values:
c = 83,680 J / (100 kg * 80 K)
Calculating the specific heat capacity:
c = 104.6 J/(kg·K)
Therefore, the specific heat capacity of the metal is 104.6 J/(kg·K).
20kcal=100kg*c*80 C
c=20k/(100k*8O)=.2/80=.02/8
= .0025 cal/g-C
20 kcal =83736 J
Q=cmΔT
c=Q/mΔT