Determine the final temperature when 100 g of water absorbs 1000 J of thermal energy, given that the initial temperature of the water is 20.0°C. The theoretical specific heat capacity of water is 4.19 J/g°C.
To determine the final temperature, we can use the equation:
q = mcΔT
Where:
- q is the thermal energy absorbed/released by the substance (in this case, water) (Joules)
- m is the mass of the substance (in this case, water) (grams)
- c is the specific heat capacity of the substance (J/g°C)
- ΔT is the change in temperature (final temperature - initial temperature) (°C)
Rearranging the equation to solve for ΔT, we have:
ΔT = q / (mc)
Substituting the given values:
q = 1000 J
m = 100 g
c = 4.19 J/g°C
ΔT = 1000 J / (100 g * 4.19 J/g°C)
Calculating ΔT:
ΔT = 1000 J / 419 J/°C
ΔT ≈ 2.39 °C
To find the final temperature, we add the change in temperature to the initial temperature:
Final temperature = Initial temperature + ΔT
Final temperature = 20.0°C + 2.39°C
Final temperature ≈ 22.29°C
Therefore, the final temperature is approximately 22.29°C.