Respuesta :
Answer:
The amount of entropy produced by the quenching process is 0.303 kJ/K.
Explanation:
Given that,
Mass = 2.5 kg
Temperature = 800°C
The mass of 50 L of water is 50 kg
Temperature = 20°C
Energy = 4.18 kJ/kg.K
If the final temperature of the metal bar and water is T₀°C, then
The heat lost by the bar = heat gained by water
[tex]m_{w}C_{w}(T_{0}-T)=m_{B}c_{B}(T-T_{0})[/tex]
Put the value into the formula
[tex]4.18\times50(T-20)=0.5\times2.5(80-T)[/tex]
[tex]209T-4180=1000-1.25T[/tex]
[tex]210.25T=5180[/tex]
[tex]T=\dfrac{5180}{210.25}[/tex]
[tex]T=24.64^{\circ}C[/tex]
Now, heat exchange between the systems
[tex]\Delta Q=m_{w}C_{w}(T-20)[/tex]
[tex]\Delta Q=4.18\times50(24.64-20)[/tex]
[tex]\Delta Q=969.76\ kJ[/tex]
We need to calculate the entropy
Using formula of entropy
[tex]S=\dfrac{\Delta Q}{\dfrac{T+T_{0}}{2}+T'}-\dfrac{\Delta Q}{\dfrac{T+T_{0}}{2}+T'}[/tex]
Where, T' = 273.15\ K
Put the value into the formula
[tex]S=\dfrac{969.76}{\dfrac{20+24.64}{2}+273.15}}-\dfrac{969.76}{\dfrac{80+24.64}{2}+273.15}[/tex]
[tex]S=3.28209293668-2.97956800934[/tex]
[tex]S=0.303\ kJ/K[/tex]
Hence, The amount of entropy produced by the quenching process is 0.303 kJ/K.
