A sample of `0.16 g CH_(4)` was subjected to combustion at `27^(@)C` in a bomb calorimeter. The temperature of the calorimeter system (including water) was found to rise by `0.5^(@)C`. Calculate the heat of combustion of methane at (a) constant volume and (b) constant pressure. The thermal capacity of calorimeter system is `17.7 kJ K^(-1)` and `R = 8.314 J K^(-1) mol^(-1)`.

Explanation

To solve the problem of calculating the heat of combustion of methane at constant volume and constant pressure, we will follow these steps:

### Given Data:
- Mass of methane (CH₄) = 0.16 g
- Temperature rise (ΔT) = 0.5 °C
- Thermal capacity of calorimeter (C) = 17.7 kJ/K
- Gas constant (R) = 8.314 J/(K·mol)
- Molecular mass of CH₄ = 16 g/mol
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