what would be the final amount of water in a mixture when 2kg ice at -20 degrees celsius is mixed with 5kg water at 20 degrees celsius? Given:specific heat capacity of ice=0.5/gram degree celsius,specific heat capacity of water=1cal/gram degree celsius,latent heat of fusion of ice=80 cal/grams
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To find the final amount of water in the mixture, we need to consider the heat exchange between the ice and water during the process.
Here's how we can calculate it step by step:
Step 1: Calculate the heat absorbed by the ice to reach 0 degrees Celsius (the melting point of ice):
Heat absorbed by ice = mass of ice × specific heat capacity of ice × change in temperature
Since the ice is originally at -20 degrees Celsius and needs to reach 0 degrees Celsius:
Heat absorbed by ice = 2 kg × 0.5 cal/g°C × (0 - (-20)°C)
= 2 kg × 0.5 cal/g°C × 20°C
= 20 cal/g × 2 kg
= 40 cal
Step 2: Calculate the heat absorbed by the ice to melt completely into water:
Heat absorbed by ice = mass of ice × latent heat of fusion of ice
Heat absorbed by ice = 2 kg × 80 cal/g
= 160 cal
Step 3: Calculate the heat absorbed by the water to reach the final temperature (taken by the ice):
Heat absorbed by water = mass of water × specific heat capacity of water × change in temperature
The water is initially at 20 degrees Celsius and needs to reach 0 degrees Celsius:
Heat absorbed by water = 5 kg × 1 cal/g°C × (0 - 20)°C
= 5 kg × 1 cal/g°C × (-20)°C
= -100 cal
Step 4: Calculate the final amount of water in the mixture:
Final amount of water = mass of water + mass gained from the melted ice
Since the ice has melted completely into water, the mass gained from the ice is equal to the mass of ice, which is 2 kg.
Final amount of water = 5 kg + 2 kg
= 7 kg
Therefore, the final amount of water in the mixture is 7 kg.