calculate heat capacity of a bituminous coal that has the following ultimate analysis: 81.3% c; 5.3% h; 9.8% o; 1.7% n; 1.9% s.

To calculate the heat capacity of bituminous coal, we need to know the specific heat capacities of its components. The specific heat capacities of carbon (C), hydrogen (H), oxygen (O), nitrogen (N), and sulfur (S) are approximately 0.709, 14.304, 0.918, 1.04, and 0.71 J/g°C, respectively.

The heat capacity of the coal can be calculated by multiplying the percentage of each element by its specific heat capacity and then adding all these values together.

Here's the step-by-step calculation:

1. Calculate the heat capacity contribution from each element:

   • Carbon (C): 81.3% * 0.709 J/g°C = 57.6 J/g°C
   • Hydrogen (H): 5.3% * 14.304 J/g°C = 0.76 J/g°C
   • Oxygen (O): 9.8% * 0.918 J/g°C = 9.0 J/g°C
   • Nitrogen (N): 1.7% * 1.04 J/g°C = 0.02 J/g°C
   • Sulfur (S): 1.9% * 0.71 J/g°C = 0.01 J/g°C

2. Add all these values together to get the total heat capacity of the coal:

   Total heat capacity = 57.6 J/g°C + 0.76 J/g°C + 9.0 J/g°C + 0.02 J/g°C + 0.01 J/g°C = 67.39 J/g°C

So, the heat capacity of the bituminous coal is approximately 67.39 J/g°C.