Question

A 50kg block of nickel at 90°C is dropped into an insulated tank that contains 0.5 m3 of liquid water at 25°C. Determine the following. a)-Is this a control volume or closed system? b)- What is the specific heat of nickel? c)-What is the specific heat of liquid water? d)-What is the temperature when thermal equilibrium has been reached?

Answer 1

Answer:

a).Control volume

b). $C_{nickel}$ = 502.416 J/kg-K

c).  $C_{water}$ = 4.187 kJ/kg-K

d). $T_{2}$ = 87.91°C

Explanation:

a). It is a control volume system because mass is varying in the system.

b). Specific heat of nickel is $C_{nickel}$ =   502.416 J/kg-K

c). Specific heat of water is  $C_{water}$ = 4.187 kJ/kg-K

d).We know that

   net  energy transfer = change in internal energy

$m_{nickel}\times c_{nickel}(T_{2}-T_{nickel})=m_{water}\times c_{water}(T_{2}-T_{water})$

$m_{nickel}\times c_{nickel}(T_{2}-T_{nickel})=(volume_{water}\times density_{water})\times c_{water}(T_{2}-T_{water})$

$50\times 502.416\times (T_{2}-90)=(0.5\times 1000)\times 4.187\times (T_{2}-25)$

$25120.8\times (T_{2}-90)=2093.5\times (T_{2}-25)$

$T_{2}$ = 87.91°C

Answer 2

Answer:

a) Control Volume

b) 0.44 kJ/kg/K

c) 4.18 kJ/kg/K

d) 32°C

Explanation:

a. The system is a control volume because mass can be added and removed from the system.

b) Nickel has a heat capacity of 0.44 kJ/kgK

c) The heat capacity of water at standard conditions is 4.18 kJ/kgK

d)

The thermal equilibrium means that the system heat transfer of the nickel and the water are the same:

$Q_{water}=Q_{nickel}$

$m_{nickel}\cdot{c_{nickel}}\cdot{c_{nickel}}\cdot{T_{2}-T_{nickel}}=m_{water}\cdot{c_{water}}\cdot{T_{2}-T_{water}}$

$m_{nickel}\cdot{c_{nickel}}\cdot{c_{nickel}}\cdot{T_{2}-T_{nickel}}=density_{water}\cdot{volume_{water}}\cdot{c_{water}}\cdot{c_{water}}\cdot{T_{2}-T_{water}}$

$50\cdot{0.44}\cdot{(T_2-363)}=0.5\cdot{1000}\cdot{4.18}\cdot{(T_2-298)}$

$T_2=305.03$

The temperature will be 305.03 K which is 32°C