Respuesta :
Answer:
[tex]m_l=0.619\ kg[/tex]
Explanation:
Given:
- initial temperature of water(lemonade), [tex]T_{il}=20.5^{\circ}C[/tex]
- mass of ice, [tex]m=0.055\ kg[/tex]
- initial temperature of ice, [tex]T_{ii}=-10.2^{\circ}C[/tex]
- final temperature of the mixture, [tex]T_f=11.8^{\circ}C[/tex]
- specific heat capacity of ice, [tex]c_i=2000\ J.kg^{-1}. ^{\circ}C^{-1}[/tex]
- specific heat capacity of water, [tex]c_w=4186\ J.kg^{-1}. ^{\circ}C^{-1}[/tex]
- Latent heat of fusion of ice, [tex]L=340000\ J.kg^{-1}[/tex]
For the whole ice to melt in lemonade and result a temperature of 11.8°C the total heat lost by the lemonade will be equal to the total heat absorbed by the ice to come to 0°C from -10.2°C along with the latent heat absorbed in the melting of ice at 0°C and the heat absorbed by the ice water of 0°C to reach a temperature of 11.8°C.
Now, mathematically:
[tex]Q_l=Q_i+Q_m+Q_w[/tex]
[tex]m_l.c_w.\Delta T_l=m_i.c_i.\Delta T_i_i+m_i.L+m_i.c_w.\Delta T_w[/tex]
[tex]m_l.c_w.(T_{il}-T_f)=m_i(c_i.\Delta T_i_i+L+c_w.\Delta T_w)[/tex]
[tex]m_l\times 4186\times (20.5-11.8)=0.055(2000\times (0-(-10.2))+340000+4186\times (11.8-0))[/tex]
[tex]m_l=0.619\ kg[/tex] (mass of lemonade)