Respuesta :
Answer : The temperature of the coffee after the ice melts is [tex]100.5^oC[/tex]
Explanation :
In this question we have to determine the temperature of the coffee after the ice melts.
Heat lost by coffee = Heat gained by ice
[tex]m_1\times c_1\times (T_f-T_1)=-m_2\times c_2\times (T_f-T_2)+n\times \Delta H_{fus}[/tex]
where,
[tex]c_1[/tex] = specific heat of coffee = specific heat of water = [tex]4.18J/g^oC[/tex] (as per question)
[tex]c_2[/tex] = specific heat of ice = [tex]2.01J/g^oC[/tex]
[tex]m_1[/tex] = mass of coffee = 110 g
[tex]m_2[/tex] = mass of ice = 9.0 g
[tex]T_f[/tex] = final temperature = ?
[tex]T_1[/tex] = initial temperature of coffee = [tex]90^oC[/tex]
[tex]T_2[/tex] = initial temperature of ice = [tex]0^oC[/tex]
n = number of moles of ice = [tex]\frac{9.0g}{18g/mole}=0.5mole[/tex]
[tex]\Delta H_{fus}[/tex] = 6.0 kJ/mol = 6000 J/mol
Now put all the given values in the above formula, we get
[tex]110g\times 4.18J/g^oC\times (T_f-90)^oC=-9.0g\times 2.01J/g^oC\times (T_f-0)^oC+0.5mol\times 6000J/mol[/tex]
[tex]T_f=100.5^oC[/tex]
Therefore, the temperature of the coffee after the ice melts is [tex]100.5^oC[/tex]
