Answer:
a) All ice melts
b) Final temperature = 10.6°C
Step-by-step explanation:
Given Data:
mass of ice = 0.50 kg
temperature = -20°C
placed in a cup containing 3.5kg of water that is at 25°c
A) Determine if all the ice melts
3.5 kg of 25°c water to 0°c
Heat rejected = 3.5 * 10^3 * 1 * 25 cal = 87500 cal
0.5 kg - 20°c ice to 0°c ice
Heat gained = 0.5 * 0.5 * 10^3 *20 cal = 5000 cal
0.50 kg 0°c ice to 0°c water
Heat gained = 0.5 * 10^3 * 80 cal = 40000 cal
All the ice will melt eventually
B) Determine the final temperature
0°c water of 0.5kg to t°C water
heat gained = 0.5 * 10^3 * 1 * t = 500 t cal
heat rejected = 3.5*10^3 * 1 * ( 25 - t )
= 3500 ( 25 - t )
To determine the Final temperature we will equate the Total heat gained to the Total heat rejected
= 5000 + 40000 + 500 t = 3500 ( 25 - t )
= 4000 t = 3500 * (25 - 45000)
Hence t = 10.6°C