Determine the final temperature of water if 17.6 kJ of heat is added to 350 g of water initially at a temperature of 24.10 C. (specific heat of water is 4.184 Jg^-1K^-1)
17600 = 4.184 * 350 (T-24.1)
To determine the final temperature of water, we can use the formula for heat transfer:
Q = m * c * ΔT
Where:
Q is the heat transferred (in joules),
m is the mass of the water (in grams),
c is the specific heat capacity of water (in J/g·°C), and
ΔT is the change in temperature (in °C).
We are given:
Q = 17.6 kJ = 17.6 * 10^3 J (since 1 kJ = 1000 J)
m = 350 g
c = 4.184 J/g·°C
The initial temperature, Ti = 24.10 °C
Rearranging the formula, we can solve for ΔT:
ΔT = Q / (m * c)
Substituting the given values, we find:
ΔT = (17.6 * 10^3 J) / (350 g * 4.184 J/g·°C)
Calculating this expression will give us the change in temperature. Once we have obtained ΔT, we can add it to the initial temperature to find the final temperature, Tf.
Tf = Ti + ΔT
Now let's calculate ΔT:
ΔT = (17.6 * 10^3 J) / (350 g * 4.184 J/g·°C)
ΔT ≈ 11.62 °C
Finally, we can find the final temperature:
Tf = Ti + ΔT
Tf = 24.10 °C + 11.62 °C
Tf ≈ 35.72 °C
Therefore, the final temperature of the water is approximately 35.72 °C.