How Do I Solve This Chemistry Equation?

One gram of coal gives off 7000.0 calories when burned. How many joules is this? How many grams of coal are required to raise the temperature of 4.0 Liters of water from 20 degrees celsius to 100 degrees celsius? (This is supposed to be a specific heat explanation)

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Summerrae

asked 1 year ago

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(7000 calories)(4.184 J/cal_th) = 29,288 J = 29.288 kJ.

The volumetric heat capacity of water is 4.184 J/cc/K, so the amount of coal required to raise 4 l of water 80 kelvin is ...

(4.184 J/cc/K)*(80 K)*(4 l)*(1000 cc/l)*(1 g/29,288 J) = (4.184)(80)(4)(1000)/29288 g
= (80)(4)(1000)(4.184)/((7000)(4.184)) g = (80)(4)(1000)/7000 g
= 320/7 g = 45.7 g

This is an approximation. The specific heat of water varies with temperature, so the average value over the temperature range is required. The value used here appears to be a maximum.

Similarly, the mass of water represented by 4.0 liters will vary with temperature. Because the "volumetric" heat capacity of water is used, we don't worry too much about that here.

In the real world, whether or not you can actually heat water to 100^oC depends on the pressure applied, and there will be various heat losses in any real heating apparatus.