A 0.5kg piece of metal (c = 600/kgK) at 300 degree celcius is dumped into a large pool of water at 20 degrees celcius. Assuming the change in temperature of water to be negligible, calculate the overall change in entropy for the system

ΔS =ΔQ/T= cmΔT/T =

=600•0.5•280/20=4200 J/K

122.3J/k

To calculate the overall change in entropy for the system, we need to consider two components: the change in entropy of the metal and the change in entropy of the water.

1. Change in entropy of the metal:
The change in entropy of the metal can be calculated using the equation:
ΔS = m * c * ΔT / T
where ΔS is the change in entropy, m is the mass of the metal, c is the specific heat capacity of the metal, ΔT is the change in temperature, and T is the initial temperature of the metal.

In this case, the mass of the metal (m) is 0.5 kg, the specific heat capacity of the metal (c) is 600 J/kgK, and the initial temperature (T) is 300 degrees Celsius. The final temperature (Tf) of the metal is the same as the temperature of the water, which is 20 degrees Celsius. Therefore, the change in temperature (ΔT) is:
ΔT = Tf - T = 20 - 300 = -280 degrees Celsius

Now we can calculate the change in entropy of the metal:
ΔS_metal = m * c * ΔT / T
= 0.5 kg * 600 J/kgK * (-280 degrees Celsius) / (300 degrees Celsius)

2. Change in entropy of the water:
Assuming the change in temperature of the water is negligible, the change in entropy can be considered negligible as well. Hence, the change in entropy of the water is approximately zero.

Finally, the overall change in entropy for the system is the sum of the changes in entropy of the metal and the water:
ΔS_system = ΔS_metal + ΔS_water
= ΔS_metal + 0 (since the change in entropy of the water is zero)

Therefore, the overall change in entropy for the system is equal to the change in entropy of the metal:
ΔS_system = ΔS_metal