would 20.0g of steam at 100 degreeC. be enough to melt 20.0g of ice at 0 degreeC
To determine if 20.0g of steam at 100 degreeC is enough to melt 20.0g of ice at 0 degreeC, we need to compare the amount of heat energy gained by the ice to the amount of heat energy lost by the steam.
To melt ice, three steps are involved:
1. Heating the ice from 0 degreeC to the melting point.
2. Melting the ice at the melting point.
3. Heating the resulting water from the melting point to its final temperature.
Let's break down the steps and calculate the amount of heat energy required for each.
Step 1: Heating the ice
The heat energy required to heat the ice can be calculated using the specific heat capacity formula (q = mcΔT), where:
- q is the heat energy
- m is the mass of the substance (ice)
- c is the specific heat capacity of the substance (generally around 2.09 J/g°C for ice)
- ΔT is the change in temperature
q1 = m1 * c1 * ΔT1
= 20.0g * 2.09 J/g°C * (0°C - (-10°C))
= 20.0g * 2.09 J/g°C * 10°C
= 418 J
Step 2: Melting the ice
The heat energy required to melt the ice can be calculated using the enthalpy of fusion formula (q = m * ΔHf), where:
- q is the heat energy
- m is the mass of the substance (ice)
- ΔHf is the enthalpy of fusion for the substance (generally around 334 J/g for ice)
q2 = m2 * ΔHf
= 20.0g * 334 J/g
= 6680 J
Step 3: Heating the resulting water
The heat energy required to heat the resulting water can be calculated using the specific heat capacity formula (q = mcΔT), where:
- q is the heat energy
- m is the mass of the substance (water)
- c is the specific heat capacity of the substance (generally around 4.18 J/g°C for water)
- ΔT is the change in temperature
q3 = m3 * c3 * ΔT3
= 20.0g * 4.18 J/g°C * (100°C - 0°C)
= 20.0g * 4.18 J/g°C * 100°C
= 8360 J
Total heat energy required = q1 + q2 + q3
= 418 J + 6680 J + 8360 J
= 15458 J
Now, let's calculate the amount of heat energy in 20.0g of steam at 100 degreeC.
The heat energy in steam can be calculated using the specific heat capacity formula (q = mcΔT), where:
- q is the heat energy
- m is the mass of the substance (steam)
- c is the specific heat capacity of the substance (generally around 2.03 J/g°C for steam)
- ΔT is the change in temperature
q4 = m4 * c4 * ΔT4
= 20.0g * 2.03 J/g°C * (100°C - 100°C)
= 0 J
Since the heat energy in the steam is 0 J, it means that 20.0g of steam at 100 degreeC is not enough to melt 20.0g of ice at 0 degreeC.