Question

Exhaust gases having properties similar to dry air enter a thin-walled cylindrical exhaust stack at 800 K. The stack is made of steel and is 8 m tall and 0.5 m inside diameter. If the gas flow rate is 0.5 kg/s and the heat transfer coefficient at the outer surface is 16 W(m2 K), estimate the outlet temperature of the exhaust gas if the ambient temperature is 280 K. Use the properties of dry water at 650 K: specific heat (cp) 1056 J/(kg K), thermal conductivity (k) 0.0472 W/(m K), absolute viscosity () 31.965 x 106 (Ns)/m2, and Prandtl number (Pr) 0.71.

Answer 1

The actual temperature of 779 K is the better estimate compared to the estimates obtained using the ideal gas equation and Van der Waals equation of state.

Step-by-step explanation:

The correct answer is option (c), the actual temperature of 779 K is the better estimate. In part (a), the ideal gas equation is used to estimate the temperature at which 1.00 kg of steam occupies a certain volume and pressure. In part (b), the Van der Waals equation of state is used to estimate the temperature under the same conditions, taking into account the van der Waals constants for water.

estimating the outlet temperature of the exhaust gas given the initial temperature, flow rate, and properties of the exhaust gases (similar to dry air), is based on the application of the energy balance and heat transfer principles. To compute the outlet temperature, one would typically apply the formula Q = mcΔT, where Q represents the heat transfer rate, m is the mass flow rate, c is the specific heat at constant pressure, and ΔT is the change in temperature.

However, without the specific formula for this calculation provided or a more definitive dBoth estimates are compared to the actual temperature of 779 K. Since the actual temperature is closer to the estimate in part (b), it is considered the better estimate.