A piece of metal at 80 degrees celsius is placed in 1.2 L of water at 72 degrees celsius. The system is thermally isolated and reaches a final temperature of 75 degrees celsius. Estimate the approximate change in entrophy for this process.
To estimate the approximate change in entropy for this process, we first need to compute the change in heat (ΔQ) and the temperature (ΔT). We can use the formula:
ΔS = ΔQ / ΔT
1. Calculate the change in heat (ΔQ):
- Use the formula Q = m * c * ΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the temperature change.
- The metal's initial temperature is 80 degrees Celsius, the final temperature is 75 degrees Celsius, and the specific heat capacity of metal is typically lower than water. Let's assume it to be 0.5 J/g°C.
- Since we do not know the mass of the metal, let's assume it to be 100 g (you can adjust this value later). Therefore, ΔQ = 100 g * 0.5 J/g°C * (75 - 80)°C.
2. Calculate the change in temperature (ΔT) for the water:
- The initial temperature of the water is 72 degrees Celsius, and the final temperature is 75 degrees Celsius.
- Therefore, ΔT = 75°C - 72°C.
3. Now, you can calculate the approximate change in entropy (ΔS):
- ΔS = ΔQ / ΔT.
Plug in the values to calculate ΔS. The units of ΔS will depend on the units used for mass, temperature, and specific heat capacity.