Answer:
the entropy change of the copper block = - 117.29 J/K
the entropy change of the water = 138.01 J/K
the entropy change of the universe = 20.72 J/K
Explanation:
For Copper block:
the mass of copper block
= 1.00 kg
Temperature of block of copper
= 100°C
= (100+273)K
= 373K
Standard Heat capacity for copper
= 386 J/kg.K
For water:
We know our volume of liquid water to be = 4.00 L
At 0.0°C Density of liquid water = 999.9 kg/m³
As such; we can determine the mass since : ![density = \frac{mass}{volume}](https://tex.z-dn.net/?f=density%20%3D%20%5Cfrac%7Bmass%7D%7Bvolume%7D)
∴ the mass of 4.00 L of liquid water at 0.0°C will be its density × volume.
= 999.9 kg/m³ × ![\frac{4}{1000}m^3](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B1000%7Dm%5E3)
= 3.9996 kg
so, mass of liquid water
= 3.9996 kg
Temperature of liquid water
at 0.0°C = 273 K
Standard Heat Capacity of liquid water
= 4185.5 J/kg.K
Let's determine the equilibruium temperature between the copper and the liquid water. In order to do that; we have:
![m_cC_c \delta T_c =m_wC_w \delta T_w](https://tex.z-dn.net/?f=m_cC_c%20%5Cdelta%20T_c%20%3Dm_wC_w%20%5Cdelta%20T_w)
![1.00*386*(373-T_\theta)=3.996*4185.5*(T _\theta-273)](https://tex.z-dn.net/?f=1.00%2A386%2A%28373-T_%5Ctheta%29%3D3.996%2A4185.5%2A%28T%20_%5Ctheta-273%29)
![386(373-T_\theta)=16725.26(T_\theta-273)](https://tex.z-dn.net/?f=386%28373-T_%5Ctheta%29%3D16725.26%28T_%5Ctheta-273%29)
![(373-T_\theta)=\frac{16725.26}{386} (T_\theta-273)](https://tex.z-dn.net/?f=%28373-T_%5Ctheta%29%3D%5Cfrac%7B16725.26%7D%7B386%7D%20%28T_%5Ctheta-273%29)
![(373-T_\theta)=43.33 (T_\theta-273)](https://tex.z-dn.net/?f=%28373-T_%5Ctheta%29%3D43.33%20%28T_%5Ctheta-273%29)
![(373-T_\theta)=43.33 T_\theta-11829.09](https://tex.z-dn.net/?f=%28373-T_%5Ctheta%29%3D43.33%20T_%5Ctheta-11829.09)
![373+11829.09=43.33 T_\theta+T_\theta](https://tex.z-dn.net/?f=373%2B11829.09%3D43.33%20T_%5Ctheta%2BT_%5Ctheta)
![12202.09 =43.33T_\theta](https://tex.z-dn.net/?f=12202.09%20%3D43.33T_%5Ctheta)
![T_\theta= 275.26 K](https://tex.z-dn.net/?f=T_%5Ctheta%3D%20275.26%20K)
∴ the equilibrium temperature = 275.26 K
NOW, to determine the Entropy change of the copper block; we have:
![(\delta S)_{copper}=m_cC_cIn(\frac{T_\theta}{T_c} )](https://tex.z-dn.net/?f=%28%5Cdelta%20S%29_%7Bcopper%7D%3Dm_cC_cIn%28%5Cfrac%7BT_%5Ctheta%7D%7BT_c%7D%20%29)
![(\delta S)_{copper}=1.0*386In(\frac{275.26}{373} )](https://tex.z-dn.net/?f=%28%5Cdelta%20S%29_%7Bcopper%7D%3D1.0%2A386In%28%5Cfrac%7B275.26%7D%7B373%7D%20%29)
![(\delta S)_{copper}=-117.29 J/K](https://tex.z-dn.net/?f=%28%5Cdelta%20S%29_%7Bcopper%7D%3D-117.29%20J%2FK)
The entropy change of the water can also be calculated as:
![(\delta S)_{water}=m_wC_wIn(\frac{T_\theta}{T_w} )](https://tex.z-dn.net/?f=%28%5Cdelta%20S%29_%7Bwater%7D%3Dm_wC_wIn%28%5Cfrac%7BT_%5Ctheta%7D%7BT_w%7D%20%29)
![(\delta S)_{water}=3.9996*4185.5In(\frac{275.26}{373} )](https://tex.z-dn.net/?f=%28%5Cdelta%20S%29_%7Bwater%7D%3D3.9996%2A4185.5In%28%5Cfrac%7B275.26%7D%7B373%7D%20%29)
![(\delta S)_{water}=138.01J/K](https://tex.z-dn.net/?f=%28%5Cdelta%20S%29_%7Bwater%7D%3D138.01J%2FK)
The entropy change of the universe is the combination of both the entropy change of copper and water.
![(\delta S)_{universe}=(\delta S)_{copper}+(\delta S)_{water}](https://tex.z-dn.net/?f=%28%5Cdelta%20S%29_%7Buniverse%7D%3D%28%5Cdelta%20S%29_%7Bcopper%7D%2B%28%5Cdelta%20S%29_%7Bwater%7D)
![(\delta S)_{universe}=(-117.29+138.01)J/K](https://tex.z-dn.net/?f=%28%5Cdelta%20S%29_%7Buniverse%7D%3D%28-117.29%2B138.01%29J%2FK)
![(\delta S)_{universe}=20.72J/K](https://tex.z-dn.net/?f=%28%5Cdelta%20S%29_%7Buniverse%7D%3D20.72J%2FK)