When 1.60 multiplied by 105 J of heat enters a cherry pie initially at 20.0°C, its entropy increases by 470 J/K. What is its final temperature (C)?
Drwls answered:
delta S = entropy change = 1.6*10^5*[1/293 - 1/T2] = 470
Solve for T2
But after I checked the answer, it is not correct.
To find the final temperature (T2) of the cherry pie, you can use the formula provided by Drwls. However, there seems to be a small error in the formula used.
The correct formula for entropy change is:
ΔS = Q/T
Where ΔS is the change in entropy, Q is the heat added to the system, and T is the temperature in Kelvin.
Let's rewrite the formula correctly:
ΔS = 470 J/K
Q = 1.60 * 10^5 J
Now, we need to convert the initial temperature (20.0°C) to Kelvin:
T1 = 20.0°C + 273.15 = 293.15 K
Now, we can rearrange the equation to solve for the final temperature (T2):
ΔS = Q/T2
T2 = Q/ΔS
Substituting the values we have:
T2 = (1.60 * 10^5 J) / (470 J/K)
T2 ≈ 340.43 K
To convert the final temperature from Kelvin to Celsius, subtract 273.15 from the result:
T2 ≈ 340.43 K - 273.15 = 67.28°C
So, the final temperature of the cherry pie is approximately 67.28°C.