Given that the specific heat capacities of ice and steam are 2.06 J/g degrees C and 2.03 J/g degrees C, respectively, calculate the total quantity of heat evolved when 10.0 g of steam at 200 degrees C is condensed, cooled, and frozen to ice at -50 degrees C.
q1 = heat released on cooling steam from 200 C to 100 C.
q1 = mass steam x specific heat steam x (Tfinal-Tintial). Tfinal = 100, Tinitial = 200
q2 = heat released when steam is condensed at 100 C to liquid water at 100 C.
q2 = mass steam x heat vaporization
q3 = heat released in cooling liquid H2O from 100 C to zero C.
q3 = mass H2O x specific heat H2O x (Tfinal-Tinitial)
q4 = heat released on freezing water at zero C to ice at zero C.
q4 = mass water x heat fusion
q5 = heat released in cooling ice at zero C to ice at -50C.
q5 = mass ice x specific heat x (Tfinal-Tinitial)
Total Q = q1 + q2 + q3 + q4 + q5
To calculate the total quantity of heat evolved when steam is condensed, cooled, and frozen to ice, we need to consider three steps:
1. Condensation of steam to water.
2. Cooling of water from 100 degrees C to 0 degrees C.
3. Freezing of water to ice at 0 degrees C.
Let's calculate the quantity of heat evolved for each step:
Step 1: Condensation of steam to water
The change in temperature during condensation is from 100 degrees C to 0 degrees C.
The specific heat capacity of steam is 2.03 J/g degrees C.
The quantity of heat evolved during condensation can be calculated using the formula:
q = m * C * ΔT
where q is the quantity of heat evolved, m is the mass of the substance, C is the specific heat capacity, and ΔT is the change in temperature.
q1 = 10.0 g * 2.03 J/g degrees C * (100 - 0) degrees C
q1 = 2030 J
Step 2: Cooling of water from 0 degrees C to -50 degrees C
The change in temperature during cooling is from 0 degrees C to -50 degrees C.
The specific heat capacity of water is 4.18 J/g degrees C.
The quantity of heat evolved during cooling can be calculated using the same formula:
q2 = 10.0 g * 4.18 J/g degrees C * (0 - (-50)) degrees C
q2 = 2090 J
Step 3: Freezing of water to ice at 0 degrees C
The specific heat capacity of ice is 2.06 J/g degrees C.
The change in temperature during freezing is from 0 degrees C to -50 degrees C.
The quantity of heat evolved during freezing can be calculated using the same formula:
q3 = 10.0 g * 2.06 J/g degrees C * (0 - (-50)) degrees C
q3 = 1030 J
Now, to find the total quantity of heat evolved, we sum up the quantities of heat from each step:
Total quantity of heat evolved = q1 + q2 + q3
Total quantity of heat evolved = 2030 J + 2090 J + 1030 J
Total quantity of heat evolved = 5150 J
Therefore, the total quantity of heat evolved when 10.0 g of steam at 200 degrees C is condensed, cooled, and frozen to ice at -50 degrees C is 5150 J.
To calculate the total quantity of heat evolved when steam is condensed, cooled, and frozen to ice, we need to consider the different stages involved.
1. Heat evolved during condensation: When steam is condensed, it releases heat equal to the heat of vaporization, which is the heat required to convert one gram of steam to one gram of water at the same temperature. The heat of vaporization for water is 2260 J/g.
Heat evolved during condensation = Mass of steam x Heat of vaporization
Given: Mass of steam = 10.0 g
Heat of vaporization = 2260 J/g
Heat evolved during condensation = 10.0 g x 2260 J/g
2. Heat evolved during cooling: After condensation, the water needs to be cooled from the initial temperature of 200°C to 0°C. This requires removing heat equal to the specific heat capacity of steam.
Heat evolved during cooling = Mass of water x Specific heat capacity of steam x Temperature change
Given: Mass of water = 10.0 g
Specific heat capacity of steam = 2.03 J/g°C
Temperature change = 200°C - 0°C = 200°C
Heat evolved during cooling = 10.0 g x 2.03 J/g°C x 200°C
3. Heat evolved during freezing: Finally, the water at 0°C needs to be frozen to ice at -50°C. This requires removing heat equal to the specific heat capacity of ice.
Heat evolved during freezing = Mass of ice x Specific heat capacity of ice x Temperature change
Given: Mass of ice = 10.0 g
Specific heat capacity of ice = 2.06 J/g°C
Temperature change = 0°C - (-50°C) = 50°C
Heat evolved during freezing = 10.0 g x 2.06 J/g°C x 50°C
To find the total quantity of heat evolved, add up the heat evolved during each stage:
Total heat evolved = Heat evolved during condensation + Heat evolved during cooling + Heat evolved during freezing
Total heat evolved = (10.0 g x 2260 J/g) + (10.0 g x 2.03 J/g°C x 200°C) + (10.0 g x 2.06 J/g°C x 50°C)
Calculate the values and solve the expression to determine the total quantity of heat evolved.