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# Answer to Question #69008 in Inorganic Chemistry for Mohit aggarwal

Question #69008
10 g of ice at -10degree Celsius is added to 10g of water at 85 degree Celsius. What is the final temperature and amount of ice left in the system ( system is kept inside an ideal insulator
1
2017-06-24T11:04:07-0400
First, let us assume that all added ice will be melted. Thus, the heat balance will follow the equation:
m_i c_i âˆ†t_1+Î´_i m_i+m_i c_w âˆ†t_2=m_w c_w âˆ†t_3
m_i-mass of ice,m_w-mass of water,c_i-heat capacity of ice(2100 J/(kgâˆ™K)),c_w-heat capacity of water(4184 J/(kgâˆ™K)),Î´_i-melting heat capacity of ice(330 kJ/kg),âˆ†t_1-temperature change upon the heating ice from-10â„ƒ to 0â„ƒ,âˆ†t_2-temperature change upon the heating melted ice from 0â„ƒ to an unknown temperature and âˆ†t_3- temperature change upon the cooling hot water from 85â„ƒ to an unknown temperature.
Water and ice possess the same mass and can be removed from the equation:
c_i âˆ†t_1+Î´_i+c_w âˆ†t_2=c_w âˆ†t_3
,where âˆ†t_1=10â„ƒ,âˆ†t_2=t_x-t_0 and âˆ†t_3=t_85-t_x
âˆ†t_3-âˆ†t_2=t_85-t_x-t_x+t_0=t_85-2t_x
thus,t_x=(t_85âˆ™c_w-c_iâˆ™âˆ†t_1-Î´_i)/(2c_w )=0.55â„ƒ
The final temperature of the mixture will be 0.55 Â°C and this is due to the ice completely melted (all 10g).

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