10grams of ice at -10degree Celsius mixed with 100grams of water 50grams .specific heat of copper 0.09calories. The final temperature reached by mixture is?
what temperature is the copper and water at initially
To find the final temperature reached by the mixture, we can use the principle of conservation of energy, which states that the heat lost by the ice will be gained by the water and the copper.
Let's break down the steps to calculate the final temperature:
Step 1: Calculate the heat gained by the water.
The formula to calculate the heat gained or lost by an object is given by:
Q = mcΔT
Where Q is the heat gained or lost,
m is the mass of the object,
c is the specific heat capacity of the object, and
ΔT is the change in temperature.
For the water:
Mass (m) = 100 grams
Specific heat capacity (c) = 1 calorie/gram °C (This is the specific heat capacity of water)
Change in temperature (ΔT) = final temperature - initial temperature = final temperature - 50 °C
Step 2: Calculate the heat lost by the ice.
Similarly, using the same heat formula, for the ice:
Mass (m) = 10 grams
Specific heat capacity (c) = 0.5 calories/gram °C (This is the specific heat capacity of ice)
Change in temperature (ΔT) = final temperature - initial temperature = final temperature - (-10) °C
Step 3: Calculate the heat gained by the copper.
For the copper, we don't consider the change in temperature since its mass is negligible compared to the other components of the mixture. We only consider the heat gained during the cooling process.
Mass (m) = 0.05 grams (50 grams)
Specific heat capacity (c) = 0.09 calories/gram °C (Given)
Change in temperature (ΔT) = final temperature - initial temperature = final temperature - 50 °C (Taking 50 °C as the initial temperature of the copper, same as water)
Step 4: Equate the heat lost by ice to the heat gained by the water and copper.
Since the heat is conserved, we can equate the two equations as follows:
(mass of ice) × (specific heat capacity of ice) × (change in temperature of ice) = (mass of water) × (specific heat capacity of water) × (change in temperature of water) + (mass of copper) × (specific heat capacity of copper) × (change in temperature of copper)
(10g) × (0.5 cal/g°C) × (final temperature - (-10) °C) = (100g) × (1 cal/g°C) × (final temperature - 50°C) + (0.05g) × (0.09 cal/g°C) × (final temperature - 50 °C)
Now, solve this equation to find the final temperature reached by the mixture.