How much total heat in calories

Question

Please with steps

How much total heat in calories is required to raise the temperature of 5.31 g of ice at −15.0°C to water vapor at 113°C?

Refer to information below

Heat of vaporization = 540 cal/g

Heat of fusion of ice= 80. cal/g

Specific heat of steam= 0.48 cal/g . C

Specific heat of liquid water= 1.00 cal/g . C

Specific heat of ice= 0.48 cal/g . C

Total heat = what in calories????

Answer 1

Hello, Dayer,

The trick is to recognize that water goes through two phase changes and 3 different phases going from -15 to 113 C. The energy required is different in each of these 5 stages. The two phase changes (ice melting and water boiling) are calculated on the basis of heat of fusion and heat of vaporization. The constants used for phase changes have units of energy/mass (this can be in cal/gram. kJ/mole. or other units). They all involve a fixed amount of energy per unit of substance). There is no temperature change considered in a phase transition. Ice at 0 C becomes water at 0 C. Water at 100 C becomes steam at 100 C.

The other stages require energy to raise the temperature. Each phase of a substance will have a different specific heat, expressed as the energy required to raise a unit (mole, gram, etc.) of material 1 degree C.

If the specific heat of water is 1.00 cal/g*C, we can calculate how much heat is needed to raise 10 grams of water from 20C to 50C in the following manner:

Energy = (10 grams)*(1.00 cal/g*C)*(50C-20C)

Energy = (10 grams)*(1.00 cal/g*C)*(30C)

Energy = 300 cal to raise 10 grams of water from 20 to 50C

Set up a table to help keep things organized. I cannot fit my table in the response bax, so I'll try adding another answer with justthe table. I separated mine into the phase changes (1st column) and temperature changes (secnd column). The temerature changes need to incude the temperature change in the calculations. The phase changes do not include temperature as part of the calculation (note the units, cal/gram. There is no temperature. in the unit.

The phase changes are the result of multiplying the mass times the phase change constant. The temperature changes incude the temperature change(Final - Initial).

Add all the individual steps in going from -15.0 to 115 C. 3895 calories to take 5.31 grames of H₂O from -15 C to 115 C.

Bob