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The power plant furnace burns coal at the rate of 108,200 kg/hr. Air at 100.8 kPa, 28°C is supplied at the rate of 13.8 kg/kg coal. Determine the volume flow rate of air in m³/min.

Answer :

Final answer:

To determine the volume flow rate of air in m³/min for a power plant furnace burning coal, you need to multiply the rate of air supplied per kg of coal by the rate of coal consumption, convert to the correct time unit, and then apply the Ideal Gas Law equation.

Explanation:

The volume flow rate of air can be calculated using the Ideal Gas Law, which relates pressure (P), volume (V), and temperature (T) of a gas. The air is supplied at a rate of 13.8 kg of air per kg of coal, and the coal is burned at a rate of 108,200 kg/hr. First, we convert the air supply rate to a total air supply by multiplying 13.8 kg air/kg coal by 108,200 kg coal/hr to get the total mass flow rate of air. Then, using the Ideal Gas Law in the form PV = mRT (where m is the mass flow rate, R is the specific gas constant for air, and T is the absolute temperature in Kelvins), we can calculate the volume flow rate. However, additional information such as the specific gas constant for air would be needed to provide an actual numerical answer.

For example, assuming the specific gas constant for air is about 287 J/(kg·K), and converting the temperature to Kelvin (28°C = 301 K), you would follow these steps:

  • Calculate the total mass flow rate of air: 13.8 kg air/kg coal × 108200 kg coal/hr = 1493240 kg/hr.
  • Convert the mass flow rate to flow rate per minute: 1493240 kg/hr ÷ 60 min/hr = 24887 kg/min.
  • Use the Ideal Gas Law to solve for V, where V = mRT/P. Plug in the values: V = (24887 kg/min × 287 J/(kg·K) × 301 K) / (100.8 KPa × 1000 Pa/KPa).
  • Calculate the volume flow rate and convert it to cubic meters.

The actual volume flow rate of air can be calculated when the constants are applied.

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