Question

We have an exhaust gas that comes off a process plant at 90°C, and the process design team suggested using this exhaust gas to heat water from 15°C to 65°C by passing it over a bundle of 4 meters long and 0.01m diameter tubes through which the hot exhaust gas is flowing. The tubes are assumed to be thin-walled. Water approaches the hot exhaust gas tube bundle in the normal direction at a mean velocity of 0.8 m/s. The tubes are arranged in-line (aligned) with a transverse pitch of 30 mm and a longitudinal pitch of 40 mm. There are 10 tubes per row (nt) but the number of tube rows (nl) in the flow direction is to be determined for the proposed design. Determine nl and the pressure drop across the tube banks.

Answer 1

The maximum theoretical efficiency of a heat engine operating between temperatures of 300°C and 27°C is 47.6%, calculated using the Carnot efficiency formula after converting temperatures to Kelvin.

Step-by-step explanation:

The question provided falls under the field of Engineering, specifically focusing on heat transfer and thermodynamics within the context of a heat engine operating at a power plant. The answer involves calculating the maximum theoretical efficiency for a heat engine, which can be determined using the Carnot efficiency formula:

Efficiency (Effc) = 1 - (Tc/Th)

Where Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir. It is important to convert the given temperatures from Celsius to Kelvin. The Carnot efficiency provides an ideal upper limit to the efficiency of any real engine. The efficiency calculation does not depend on specific details such as the number of tubes or pipe arrangements, but rather on the temperatures of the heat reservoirs involved in the heat engine cycle.

The given temperatures are 300°C for the hot reservoir, which converts to 573.15K, and 27°C for the cold reservoir, converting to 300.15K. The maximum theoretical efficiency for the heat engine operating between these temperatures is:

Effc = 1 - (300.15 / 573.15) = 0.476 or 47.6%

This means that the best a heat engine at this power plant could theoretically do is convert 47.6% of the heat absorbed from the hot reservoir into work.