An electrical heater is used to supply 200.0 J of energy to a 30.0 g sample of water, originally at 285.0 K. Determine the final temperature in degrees Kelvin. (the specific heat capacity for water is 75.291 Jmol-1K-1)

q = mass x specific heat x (Tfinal-Tinitial)

Remember to change mass H2O to mols H2O if you use sp.h. in J/mol

To determine the final temperature in Kelvin, we need to understand the concept of heat transfer and specific heat capacity.

The formula for heat transfer is:

Q = m * c * ΔT

Where:
Q = amount of heat transferred
m = mass of the substance (in grams)
c = specific heat capacity (in J/molK)
ΔT = change in temperature (in Kelvin)

Given:
Q = 200.0 J
m = 30.0 g
c = 75.291 J/molK
Initial temperature (Ti) = 285.0 K

First, we need to convert the mass from grams (g) to moles (mol) since the specific heat capacity is given as J/molK.

To convert grams to moles, we use the molar mass of water (H₂O), which is approximately 18.015 g/mol:
moles = mass (g) / molar mass (g/mol)
moles = 30.0 g / 18.015 g/mol
moles ≈ 1.665 mol

Now, we can use the formula for heat transfer to find the change in temperature (ΔT):

Q = m * c * ΔT
ΔT = Q / (m * c)
ΔT = 200.0 J / (1.665 mol * 75.291 J/molK)
ΔT ≈ 1.593 K

Finally, we can calculate the final temperature (Tf) by adding the change in temperature (ΔT) to the initial temperature (Ti):

Tf = Ti + ΔT
Tf = 285.0 K + 1.593 K
Tf ≈ 286.593 K

Therefore, the final temperature is approximately 286.593 K.