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?
To determine the final temperature of the cherry pie, we can use the formula for entropy change:
∆S = Q / T
Where:
∆S is the change in entropy (in J/K)
Q is the heat transferred (in J)
T is the temperature (in K)
We are given:
Q = 1.60 * 105 J (heat)
∆S = 470 J/K (entropy change)
Initial temperature, Ti = 20.0°C
First, we need to convert the initial temperature to Kelvin:
Ti(K) = Ti(°C) + 273.15
Ti(K) = 20.0 + 273.15 = 293.15 K
Now we can rearrange the formula to solve for the final temperature (Tf):
∆S = Q / T
∆S * T = Q
Tf = Q / ∆S
Substituting the given values:
Tf = (1.60 * 105 J) / (470 J/K)
Tf ≈ 340.42 K
Therefore, the final temperature of the cherry pie is approximately 340.42 K.