Two hundred grams of a substance requires 0.52 kJ of heat to raise its temperature from 25°C to 45°C. q = mCT. Mass (m) is in grams. Temperature is in degrees Celsius.
To find the specific heat capacity (C) of the substance, we can rearrange the formula q = mCT to solve for C.
First, convert the mass from grams to kilograms by dividing by 1000:
m = 200 grams = 200/1000 = 0.2 kg
Next, calculate the change in temperature (ΔT):
ΔT = final temperature - initial temperature
ΔT = (45°C - 25°C) = 20°C
Now, substitute the given values into the formula and solve for C:
q = mCT
0.52 kJ = (0.2 kg) * C * (20°C)
To find C, divide both sides of the equation by (0.2 kg * 20°C):
C = (0.52 kJ) / (0.2 kg * 20°C)
Finally, calculate the value for C:
C = 0.52 kJ / (0.2 kg * 20°C)
C ≈ 0.13 kJ/(kg·°C)
Therefore, the specific heat capacity of the substance is approximately 0.13 kJ/(kg·°C).