A 0.60 kg chunk of ice has a temperature of -28.2o C. The pressure is one atmosphere. Heat is added to the chunk until it is completely vaporized and the steam is at a temperature of 114.4o C. How much heat was needed for this transformation?
Please i need the answer and equation to get to this answer
To determine the amount of heat needed for the transformation from solid ice to gaseous steam, you can use the heat transfer equation:
Q = m * ΔT * c,
where:
Q is the heat transfer,
m is the mass of the substance,
ΔT is the change in temperature,
c is the specific heat capacity.
First, let's calculate the heat needed to raise the temperature of the ice from -28.2o C to 0o C:
Q1 = m * ΔT1 * c1,
where:
m = 0.60 kg (mass of ice),
ΔT1 = 0o C - (-28.2o C) = 28.2o C (change in temperature),
c1 = specific heat capacity of ice.
The specific heat capacity of ice is approximately 2.09 J/g·°C. However, since the units need to be consistent, we will convert the mass of the ice from kg to grams and use the specific heat capacity of ice in J/g·°C:
c1 = 2.09 J/g·°C = 2.09 J/g·°C * (1 kg / 1000 g) = 0.00209 J/g·°C.
Now we can calculate Q1:
Q1 = (0.60 kg) * (28.2o C) * (0.00209 J/g·°C).
Next, let's calculate the heat needed for the phase change from solid ice at 0o C to liquid water at 0o C. This is known as the latent heat of fusion, and for ice, it is approximately 334 J/g.
Q2 = m * c2,
where:
m = 0.60 kg (mass of ice),
c2 = latent heat of fusion of ice.
Again, we need to use consistent units, so we convert the mass to grams:
Q2 = (0.60 kg) * (334 J/g).
Now, calculate the heat needed to raise the temperature of water from 0o C to 114.4o C:
Q3 = m * ΔT3 * c3,
where:
m = 0.60 kg (mass of water),
ΔT3 = 114.4o C - 0o C = 114.4o C (change in temperature),
c3 = specific heat capacity of water.
The specific heat capacity of water is approximately 4.18 J/g·°C.
Now we can calculate Q3:
Q3 = (0.60 kg) * (114.4o C) * (4.18 J/g·°C).
Finally, to find the total heat needed, add up all the individual heats:
Q_total = Q1 + Q2 + Q3.
By plugging the relevant values into the equations above, you'll be able to calculate the total amount of heat needed for the transformation.