How do i determine the mass of ice initially in the calorimeter when dry saturated steam is passed into 250g of a mixture of ice and water in a calorimeter of thermal capacity 45J/K when all the ice has just melted,and the mass of the content in the calorimeter has increased by 10g due to condensed steam ?
If all the ice has "just" melted, the liquid is still 0 degrees C. That is the same temperature that the ice-water mixture started out. The calorimeter also remained 0 C during the ice melting, so you can ignore its heat capacity. The 10 g of steam cooled from 100 to 0 C and released 540*10 + 100*10 = 6400 calories to the icewater. That is enough heat to just melt 6400/80 = 80 g of ice.
80 g of ice was initially present.
The amount of icewater initially present and the heat capacity of the calorimeter were not needed in this case.
To determine the mass of ice initially in the calorimeter, you need to use the principle of energy conservation. Here's a step-by-step guide:
Step 1: Calculate the heat absorbed by the calorimeter.
The heat absorbed by the calorimeter can be calculated using the equation: Q = mcΔT, where Q is the heat absorbed, m is the mass of the calorimeter, and ΔT is the change in temperature.
Given:
- Thermal capacity of the calorimeter (C) = 45 J/K
- Change in temperature (ΔT) = 0 K (the calorimeter remains at the same temperature)
- Mass of the calorimeter (m) = unknown
Since there is no change in temperature, the heat absorbed by the calorimeter can be calculated as:
Q = C * ΔT = 45 J/K * 0 K = 0 J
Step 2: Calculate the heat gained by the condensed steam.
The heat gained by the condensed steam can also be calculated using the equation Q = mcΔT. However, since we are given the mass of the condensed steam (10 g), we need to determine its specific heat capacity (c).
Given:
- Mass of the condensed steam (m) = 10 g
- Change in temperature (ΔT) = unknown
- Specific heat capacity of steam (c) = unknown
Step 3: Calculate the heat absorbed by the ice to melt it.
The heat absorbed by the ice can be calculated using the equation Q = mL, where Q is the heat absorbed, m is the mass of the ice, and L is the latent heat of fusion of ice.
Given:
- Change in mass of the content in the calorimeter (Δm) = 10 g (due to condensed steam)
- Specific latent heat of fusion of ice (L) = 334 kJ/kg = 334000 J/kg
Using the formula Q = mL, we can calculate the heat absorbed by the ice:
Q = Δm * L = 10 g * (334000 J/kg / 1000 g/kg) = 3340 J
Step 4: Apply the principle of energy conservation.
According to the principle of energy conservation, the heat absorbed by the calorimeter should be equal to the sum of the heat gained by the condensed steam and the heat absorbed by the ice.
Hence, combining the results of Step 1, Step 2, and Step 3:
0 J = mcΔT + mcΔT + mL
Since the calorimeter and the condensed steam have gained heat but not changed temperature, their mass can be ignored. The equation can be simplified to:
0 J = mL
Since the heat absorbed is equal to the heat gained by the ice, we can determine the mass of the ice as:
m = Q / L = 3340 J / (334000 J/kg / 1000 g/kg) = 10 g
Therefore, the mass of ice initially in the calorimeter is 10 g.
To determine the mass of ice initially in the calorimeter, we can use the principle of energy conservation. Here are the steps to find the mass of ice:
1. Calculate the heat absorbed by the calorimeter:
The change in energy (ΔQ) of the calorimeter is given by:
ΔQ = mcΔT
where m is the mass of the calorimeter, c is the specific heat capacity of the calorimeter material, and ΔT is the change in temperature. In this case, the change in temperature is zero since the ice has just melted.
ΔQ = mc × 0 = 0
2. Calculate the heat released by the condensing steam:
The heat released by the condensing steam can be calculated using the formula:
Q = mL
where m is the mass of the condensed steam and L is the latent heat of condensation.
3. Calculate the heat absorbed by the ice to melt:
The heat absorbed by the ice to melt can be calculated using the formula:
Q = m × (Hf + c × ΔT)
where m is the mass of the ice, Hf is the latent heat of fusion, c is the specific heat capacity of ice, and ΔT is the change in temperature. In this case, the change in temperature is also zero.
4. Set up the energy conservation equation:
Since energy is conserved, the heat absorbed by the ice to melt should be equal to the heat released by the condensing steam:
m × (Hf + c × ΔT) = mL
5. Solve for the mass of ice (m):
Rearrange the equation to solve for the mass of ice:
m = mL / (Hf + c × ΔT)
Substitute the given values:
m = (0.01 kg) × (2260 kJ/kg + 4.18 kJ/kg°C × 0°C) / (334 kJ/kg)
Simplify and calculate to find the mass of ice.
Following these steps and substituting the given values, you can determine the mass of ice initially in the calorimeter.