How much energy is needed to convert 90g of water (ice) at -85 degrees C to water (liquid) at 48 degree C?

Two formulas will get this for you.

For changes in temperature WITHIN a phase use q = mass x specific heat x (Tfinal-Tinitial).
example:for liquid water from zero C to 100 C. it will be q = mass H2O x specific heat H2O x (100-0)

For changes at the phase change use
q = mass x heat fusion at the melting point.
q = mass x heat vaporization at the boiling point.

Then add all of the qs together for total Q.
Post your work if you get stuck.

To calculate the energy needed to convert a substance from one state to another, we need to consider the following steps:

1. Calculate the energy required to heat the ice from its initial temperature, -85 degrees Celsius, to its melting point (0 degrees Celsius).
2. Calculate the energy required to melt the ice into water at its melting point.
3. Calculate the energy required to heat the water from its melting point to its final temperature, 48 degrees Celsius.

For each step, we will use the specific heat capacity and the heat of fusion values for water.

Step 1: Heating the ice from -85°C to 0°C

The specific heat capacity of ice is 2.09 J/g°C. Therefore, the energy required to heat the ice can be calculated using the formula:

Energy = mass × specific heat capacity × temperature change

Given: mass = 90 g, specific heat capacity = 2.09 J/g°C, initial temperature = -85°C, final temperature = 0°C

Energy = 90 g × 2.09 J/g°C × (0°C - (-85)°C)
Energy = 90 g × 2.09 J/g°C × 85°C
Energy = 1604.65 J

So, it takes approximately 1604.65 Joules of energy to heat 90 grams of ice from -85 degrees Celsius to 0 degrees Celsius.

Step 2: Melting the ice at 0°C

The heat of fusion, or the amount of energy required to convert a substance from solid to liquid at its melting point, is 334 J/g for water. Therefore, the energy required to melt the ice can be calculated using the formula:

Energy = mass × heat of fusion

Given: mass = 90 g, heat of fusion = 334 J/g

Energy = 90 g × 334 J/g
Energy = 30060 J

So, it takes approximately 30060 Joules of energy to melt 90 grams of ice at 0 degrees Celsius.

Step 3: Heating the water from 0°C to 48°C

The specific heat capacity of water is 4.18 J/g°C. Therefore, the energy required to heat the water can be calculated using the formula:

Energy = mass × specific heat capacity × temperature change

Given: mass = 90 g, specific heat capacity = 4.18 J/g°C, initial temperature = 0°C, final temperature = 48°C

Energy = 90 g × 4.18 J/g°C × (48°C - 0°C)
Energy = 17673.6 J

So, it takes approximately 17673.6 Joules of energy to heat 90 grams of water from 0 degrees Celsius to 48 degrees Celsius.

To find the total energy needed, we add up the energies from each step:

Total energy = Energy for Step 1 + Energy for Step 2 + Energy for Step 3
Total energy = 1604.65 J + 30060 J + 17673.6 J
Total energy = 49338.25 J

Therefore, it takes approximately 49338.25 Joules of energy to convert 90 grams of water (ice) at -85 degrees Celsius to water (liquid) at 48 degrees Celsius.

To calculate the amount of energy needed to convert a substance from one state to another, we need to consider the following steps:

1. Heat the ice from its initial temperature, -85 degrees C, to its melting point, 0 degrees C.
2. Calculate the energy required to melt the ice at 0 degrees C.
3. Heat the resulting water from its melting point to its final temperature, 48 degrees C.

Let's calculate the amount of energy needed for each step:

Step 1: Heating the ice from -85 degrees C to 0 degrees C.
The specific heat capacity of ice is 2.09 J/g°C.

Energy = mass × specific heat capacity × change in temperature
Energy = 90 g × 2.09 J/g°C × (0°C - (-85°C))
Energy = 90 g × 2.09 J/g°C × 85°C
Energy = 1600.7 J

Step 2: Melting the ice at 0 degrees C.
The enthalpy of fusion for water is 334 J/g.

Energy = mass × enthalpy of fusion
Energy = 90 g × 334 J/g
Energy = 30060 J

Step 3: Heating the resulting water from 0 degrees C to 48 degrees C.
The specific heat capacity of water is 4.18 J/g°C.

Energy = mass × specific heat capacity × change in temperature
Energy = 90 g × 4.18 J/g°C × (48°C - 0°C)
Energy = 90 g × 4.18 J/g°C × 48°C
Energy = 18134.4 J

Finally, we can add up the energy required for each step to get the total energy:

Total Energy = Energy for step 1 + Energy for step 2 + Energy for step 3
Total Energy = 1600.7 J + 30060 J + 18134.4 J
Total Energy ≈ 49895.1 J

Therefore, approximately 49895.1 J of energy is needed to convert 90g of ice at -85 degrees C to water at 48 degrees C.