Respuesta :
Answer: Final temperature is 34.15Ā°C.
Explanation: When two objects have different temperature, they will exchange heat energy until there is no more net energy transfer between them. At that state, the objects are in thermal equilibrium.
So, when in equilibrium, the total heat flow must be zero, i.e.:
[tex]Q_{1}+Q_{2}=0[/tex]
In our case, there will be a change in state of ice into water, so total heat flow will be:
[tex]m_{1}c_{1}(T_{f}-T_{i})+m_{2}c_{2}(T_{f}-T_{i})+mL=0[/tex]
where
mā is mass of ice
mā is mass of water
cā is specific heat of ice
cā is specific heat of water
[tex]T_{f}[/tex] is final temperature
[tex]T_{i}[/tex] is initial temperature
L is latent heat fusion
Temperature is in Kelvin so the transformation from Celsius to Kelvin:
For ice:
T = -15 + 273 = 258K
For water:
T = 48 + 273 = 321K
Solving:
[tex]21(2.09)(T_{f}-258)+158(4.186)(T_{f}-321)+21(333)=0[/tex]
[tex]43.89T_{f}-11323.62+661.4T_{f}-212305.55+6993=0[/tex]
[tex]705.3T_{f}=216636.17[/tex]
[tex]T_{f}=[/tex] 307.15K
In Celsius:
[tex]T_{f}=[/tex] 34.15Ā°C
Final temperature of the system when in equilibrium is 34.15Ā°C
