How do i determine the rise in temperature when the passage of steam is continued until a further 15g of steam has condensed and the mixture is in thermal equilibrium when dry saturated steam at 100 degrees C is passed into 25g of a mixture of ice and water contained in a calorimeter of thermal capacity of 45J/K.When all the ice has just melted,the mass of the content of the calorimeter has increased by 10g due to condensed steam
To determine the rise in temperature, we need to consider the heat gained by the ice and water mixture and the heat lost by the steam.
Let's break down the problem into smaller steps and calculate each part separately:
1. Calculate the heat gained by the ice and water mixture:
The heat gained by the ice and water mixture can be calculated using the formula:
Q = m * C * ΔT
Where:
Q is the heat gained (in Joules)
m is the mass of the mixture (in kilograms)
C is the specific heat capacity of the mixture (in J/kg°C)
ΔT is the change in temperature (in °C)
In this case, the mass of the mixture is 25g + 10g = 35g (since the mass of the content of the calorimeter increased by 10g due to condensed steam), which is equal to 0.035kg.
As we have a mixture of ice and water, we need to consider two separate phases. The specific heat capacity of ice (Cice) is 2.09 J/g°C and the specific heat capacity of water (Cwater) is 4.18 J/g°C.
Next, we calculate the heat gained when the ice melts:
m_ice = 25g
ΔT_ice = 0°C - (-0°C) = 0°C (the ice melts at 0°C)
Q_ice = m_ice * Cice * ΔT_ice
Then, we calculate the heat gained by the water:
m_water = 10g
ΔT_water = T_equilibrium - 0°C (where T_equilibrium is the final temperature when the ice has melted and the mixture is in thermal equilibrium)
Q_water = m_water * Cwater * ΔT_water
2. Calculate the heat lost by the steam:
The heat lost by the steam can be calculated using the formula:
Q = m * L
Where:
Q is the heat lost (in Joules)
m is the mass of the steam (in kilograms)
L is the latent heat of vaporization of water (in J/kg)
The latent heat of vaporization of water is 2260 J/g.
The mass of the steam condensed is 15g, which is equal to 0.015kg.
Q_steam = m_steam * L
3. Equate the heat gained and lost:
Since we have reached thermal equilibrium, the heat lost by the steam should be equal to the heat gained by the ice and water mixture.
Q_steam = Q_ice + Q_water
Now, we can rearrange the equation to solve for ΔT_water:
ΔT_water = (Q_steam - Q_ice) / (m_water * Cwater)
Finally, we can substitute the known values into the equation and calculate the rise in temperature (ΔT_water).
To determine the rise in temperature, we can follow these steps:
Step 1: Calculate the heat gained by the ice and water.
The heat gained by the ice and water can be calculated using the equation:
Q1 = m1 * c1 * ΔT1
Where:
Q1 = heat gained by the ice and water
m1 = mass of the ice and water (25g)
c1 = specific heat capacity of water (4.18 J/g°C)
ΔT1 = change in temperature of the ice and water
Since the ice melts at 0°C and the final temperature is unknown, ΔT1 will be the rise in temperature.
Step 2: Calculate the heat gained by the calorimeter.
The heat gained by the calorimeter can be calculated using the equation:
Q2 = C * ΔT2
Where:
Q2 = heat gained by the calorimeter
C = thermal capacity of the calorimeter (45 J/K)
ΔT2 = change in temperature of the calorimeter
Since the initial and final temperatures of the calorimeter are unknown, ΔT2 will be the rise in temperature.
Step 3: Calculate the heat gained by the condensed steam.
The heat gained by the condensed steam can be calculated using the equation:
Q3 = m3 * L
Q3 = heat gained by the condensed steam
m3 = mass of the condensed steam (15g)
L = latent heat of vaporization of water (2260 J/g)
Step 4: Calculate the total heat gained by the system.
The total heat gained by the system (ice, water, and calorimeter) is equal to the total heat gained by the ice and water plus the total heat gained by the calorimeter:
Q_total = Q1 + Q2
Step 5: Calculate the final temperature.
The final temperature can be calculated using the equation:
Q_total = Q3
(m1 * c1 * ΔT1) + (C * ΔT2) = (m3 * L)
Rearrange the equation to solve for ΔT1:
ΔT1 = ((m3 * L) - (C * ΔT2)) / (m1 * c1)
Step 6: Substitute the given values and calculate ΔT1.
Substitute the given values:
- m1 = 25g
- c1 = 4.18 J/g°C
- m3 = 15g
- L = 2260 J/g
- C = 45 J/K
Calculate ΔT1 using the formula:
ΔT1 = ((15g * 2260 J/g) - (45 J/K * ΔT2)) / (25g * 4.18 J/g°C)
After calculating ΔT1, you will have the rise in temperature.