a 55g aluminum block initially at 27degrees C absorbs 725J of heat. What is the final temp.
I know I need to use the equation
q=m*Cs*Delta T but I cannot figure out how to rearrange the equation to isolate Tf to get the answer.
Thanks for any help.
My experience is NOT to try rearranging it before you subtitute. I think it is far easier to substitute, then solve the equation.
q = mass x specific heat x (Tf-Ti)
725 = 55 x specific heat Al x (Tf - 27).
What Al? about 0.3 or so J/g?
725 = 55 x 0.3 x (Tf-27)
725 = 55*0.3*Tf - (55*0.3*27)
Multiply all that stuff inside the parentheses and solve the resulting equation for Tf.
To find the final temperature (Tf) of the aluminum block, we can rearrange the equation q = m * Cs * ΔT to solve for Tf.
Let's break down the equation and rearrange it step by step:
q = m * Cs * ΔT
Where:
q = heat absorbed or released (in joules)
m = mass of the substance (in grams)
Cs = specific heat capacity (in J/g°C)
ΔT = change in temperature (in °C)
Step 1: Divide both sides of the equation by (m * Cs):
q / (m * Cs) = ΔT
Step 2: Now we have isolated the ΔT. Let's substitute the given values into the equation:
ΔT = 725 J / (55 g * Cs)
Step 3: Since the specific heat capacity of aluminum is approximately 0.897 J/g°C, we can substitute this value into the equation:
ΔT = 725 J / (55 g * 0.897 J/g°C)
Step 4: Simplify the equation:
ΔT = 725 J / (48.835 g°C)
Step 5: Calculate ΔT:
ΔT ≈ 14.85 °C
Step 6: Finally, to find the final temperature (Tf), add the change in temperature (ΔT) to the initial temperature (Ti):
Tf = Ti + ΔT
Tf = 27°C + 14.85°C
Tf ≈ 41.85°C
Therefore, the final temperature of the aluminum block will be approximately 41.85°C