A piece of copper of mass 40 grams at 20 degrees Celsius is placed in a copper calorimeter of mass 60 grams containing 50 grams of water at 10 degrees Celsius .ignoring heat losses,what will be the final steady temperature after stirring?(specific heat capacity of copper and water is 0.4j/g k and 4.2j/g k
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To find the final steady temperature after stirring, we can use the principle of energy conservation.
The energy gained by the water can be calculated using the formula:
Energy gained by water = mass of water × specific heat capacity of water × change in temperature
The energy gained by the copper can be calculated using the formula:
Energy gained by copper = mass of copper × specific heat capacity of copper × change in temperature
Since no heat is lost to the surroundings, the energy gained by the water must be equal to the energy lost by the copper. Therefore, we can set these two equations equal to each other:
mass of water × specific heat capacity of water × change in temperature = mass of copper × specific heat capacity of copper × change in temperature
Now we can substitute the given values into the equation:
50 g × 4.2 J/g·K × (final temperature - 10°C) = 40 g × 0.4 J/g·K × (final temperature - 20°C)
Now, we solve this equation to find the final temperature:
(50 g × 4.2 J/g·K) × (final temperature - 10°C) = (40 g × 0.4 J/g·K) × (final temperature - 20°C)
210g·K × (final temperature - 10°C) = 16g·K × (final temperature - 20°C)
Divide both sides by (final temperature - 10°C) to isolate the final temperature:
210g·K = 16g·K × (final temperature - 20°C) / (final temperature - 10°C)
Now, we can cancel out the units (g·K) and simplify the equation:
210 = 16 × (final temperature - 20) / (final temperature - 10)
Now, cross-multiply and solve for the final temperature:
210 × (final temperature - 10) = 16 × (final temperature - 20)
210 × final temperature - 2100 = 16 × final temperature - 320
210 × final temperature - 16 × final temperature = 2100 - 320
194 × final temperature = 1780
final temperature = 1780 / 194
final temperature ≈ 9.1866°C
Therefore, the final steady temperature after stirring will be approximately 9.1866°C.