Calculate the change in entropy (in J/K) when 86.4 g of water is heated from 17.5 ºC to 76.5 ºC at 1 atm. (The specific heat is 4.184 J/(g-K).)
To calculate the change in entropy, we need to use the formula:
ΔS = q/T
where ΔS is the change in entropy, q is the heat transferred, and T is the temperature in Kelvin.
First, let's calculate the heat transferred (q) using the formula:
q = m * C * ΔT
where m is the mass of the substance, C is the specific heat capacity, and ΔT is the change in temperature.
Given information:
- Mass of water (m) = 86.4 g
- Specific heat of water (C) = 4.184 J/(g-K)
- Initial temperature (T1) = 17.5 ºC
- Final temperature (T2) = 76.5 ºC
First, we need to convert the temperatures to Kelvin by adding 273.15:
T1 = 17.5 ºC + 273.15 = 290.65 K
T2 = 76.5 ºC + 273.15 = 349.65 K
Next, we calculate the change in temperature:
ΔT = T2 - T1 = 349.65 K - 290.65 K = 59 K
Then, we calculate the heat transferred:
q = 86.4 g * 4.184 J/(g-K) * 59 K = 22,499.8784 J
Now we can calculate the change in entropy:
ΔS = q / T
Since the heat transferred (q) is in J and the temperatures (T) are in Kelvin, we can substitute these values into the formula:
ΔS = 22,499.8784 J / 349.65 K ≈ 64.286 J/K
Therefore, the change in entropy is approximately 64.286 J/K when 86.4 g of water is heated from 17.5 ºC to 76.5 ºC at 1 atm.