Question

calculate - The energy required to complete this operation (assume there is no change of phase and heat losses can be neglected).

Answer 1

Step 1 - Calculate the required heat to increase the temperature to 100°C

To calculate the amount of needed heat in passing from 15°C to 100°C, we can use the following formula, relating heat and temperature increasing:

`Q=mc\Delta T`

Since the density of water is 1g/ml (1000 kg/m^3), 900 ml equals 900g. The deltaT is 100 - 15 = 85°C and c is given (c = 4.2 J/g°C). Substituting these values:

`Q=900*4.2*85=321\text{ KJ}`

Step 2 - Calculate the heat needed to pass from liquid to vapour

We can use a similar formula, relating the needed heat to the amount of water that passed from liquid to vapour:

`Q=mC`

C is the latent heat of vaporization. For water, C= 2,256 J/g (2.256 KJ/Kg). Since only 8% of the water will evaporate, we have m = 72 g (8% of 900g). Substituting the values on the equation above:

`Q=72*2.256=162.4\text{ J}`

Step 3 - Sum up all heat contributions

Finally, we can sum up the values found in the previous steps:

`Q_{\text{total}}=321000+162.4=321.16\text{ KJ}`

The total amount of heat that would be needed would be 321.18 KJ.