A copper calorimeter weighs 100g when empty, 400g when half full of water at 0 degrees Celsius, and 450g when ice at 0 degree Celsius is added. When some steam is passed into the mixture, its temperature is raised by 10 degrees Celsius. Find the quantity of steam added
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Why did the steam go to therapy?
Because it had too many issues to condense!
But let's get to your question. To find the quantity of steam added, we need to calculate the heat gained by the copper calorimeter and the water, and then equate it to the heat lost by the steam during condensation.
First, let's calculate the heat gained by the copper calorimeter and the water. The specific heat capacity of copper is 0.385 J/g°C, and the specific heat capacity of water is 4.18 J/g°C.
Using the formula Q = mcΔT, where Q is the heat gained, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature, we can calculate the heat gained by the copper calorimeter:
Q_copper = 0.385 * 100 * 10
Next, we calculate the heat gained by the water:
Q_water = 4.18 * (400 - 100) * 10
Now, let's equate the heat gained by the copper calorimeter and the water to the heat lost by the steam during condensation:
Q_copper + Q_water = heat lost by steam
The amount of steam added can be calculated by dividing the heat lost by the steam by its specific latent heat of vaporization (L).
So, taking into consideration all of this mathematical juggling, we can calculate the quantity of steam added.
To find the quantity of steam added, we will use the principle of conservation of mass. The increase in the mass of the calorimeter after steam is added will be equal to the mass of the steam.
1. Initial mass of the copper calorimeter (empty): 100g
2. Mass of the copper calorimeter when half-full of water: 400g
3. Mass of the copper calorimeter when ice is added: 450g
Now, let's calculate the mass of the water in the calorimeter:
Mass of water = Mass of calorimeter when half-full of water - Mass of empty calorimeter
= 400g - 100g
= 300g
Next, let's calculate the heat gained by the water when it is heated from 0 degrees Celsius to 10 degrees Celsius:
Heat gained by water = Mass of water * Specific heat capacity of water * Change in temperature
= 300g * 4.18 J/g°C * 10°C
= 12540 J
Since there is no heat loss or gain in this system, the heat gained by the water is equal to the heat lost by the steam:
Heat lost by steam = Heat gained by water
= 12540 J
Now, let's assume the specific heat capacity of steam is 2.03 J/g°C. The change in temperature of the steam can be calculated using the heat lost by the steam:
Change in temperature of steam = Heat lost by steam / (Mass of steam * Specific heat capacity of steam)
= 12540 J / (Mass of steam * 2.03 J/g°C)
Finally, we need to find the mass of the steam. Rearranging the equation, we get:
Mass of steam = Heat lost by steam / (Change in temperature of steam * Specific heat capacity of steam)
Now we can plug in the known values:
Mass of steam = 12540 J / (Change in temperature of steam * 2.03 J/g°C)
Note: The specific heat capacity of water and steam can vary slightly depending on different conditions, so the above values are approximate.
Please provide the value for "Change in temperature of steam" and I will calculate the mass of steam added.
To find the quantity of steam added, we need to consider the change in heat. The heat gained by the mixture when steam is added is equal to the heat lost by the steam.
First, let's break down the problem into individual steps:
Step 1: Calculate the initial heat of the mixture (before adding steam)
Step 2: Calculate the final heat of the mixture (after adding steam)
Step 3: Calculate the heat lost by the steam
Step 4: Convert the heat lost by the steam to the quantity of steam added
Step 1: Calculate the initial heat of the mixture (before adding steam)
The initial heat of the mixture is equal to the heat gained by the water and the calorimeter. We will assume that the specific heat capacity of the copper calorimeter is negligible compared to the water.
The heat gained by the water is given by the formula:
Q = m * c * ΔT
where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Given that the half-full copper calorimeter weighs 400g and the temperature change is from 0°C to 10°C, we can calculate the heat gained by the water.
Q_water = m_water * c_water * ΔT_water
= 400g * 1 cal/g°C * 10°C
= 4000 calories
Step 2: Calculate the final heat of the mixture (after adding steam)
The final heat of the mixture is the sum of the initial heat and the heat gained by the steam.
Q_final = Q_initial + Q_steam
Step 3: Calculate the heat lost by the steam
The heat lost by the steam is given by the formula:
Q_steam = m_steam * L
where m_steam is the mass of the steam and L is the specific latent heat of vaporization.
To find the mass of the steam, we need to consider the change in mass of the mixture when the steam is added.
The change in mass is equal to the final mass of the mixture minus the initial mass of the mixture.
Change in mass = Final mass - Initial mass
= 450g - (100g + 400g)
= 50g
Since the mass of ice added is equal to the mass of water that melted, we can infer that the mass of the steam is equal to the mass of ice added.
Therefore, the mass of the steam is 50g.
Step 4: Convert the heat lost by the steam to the quantity of steam added
The heat lost by the steam (Q_steam) can be calculated using the formula:
Q_steam = m_steam * L
Given that the heat lost by the steam is equal to the initial heat of the mixture (Q_initial), we can equate the two equations:
Q_initial = m_steam * L
Substituting the values obtained:
4000 calories = 50g * L
Solving for L (specific latent heat of vaporization):
L = 4000 calories / 50g
= 80 calories per gram
Therefore, the quantity of steam added is 50g (which is equal to the mass of the ice added).