Question

In a gas-fired boiler, water is boiled at \(180^{\circ} \mathrm{C}\) by hot gases flowing through a stainless steel pipe submerged in water. If the rate of heat transfer from the hot gases to water is \(48 \mathrm{kJ} / \mathrm{s}\), determine the rate of evaporation of water.

Short answer

Answer: The rate of evaporation of water in the gas-fired boiler is approximately 0.0247 kg/s.

Step-by-step solution

Find specific latent heat of vaporization of water

To find the rate of evaporation of water, we first need to know the specific latent heat of vaporization of water (\(L_v\)). At \(180^{\circ} \mathrm{C}\), the specific latent heat of vaporization for water is approximately \(1940 \; kJ/kg\). So, \(L_v = 1940 \; kJ/kg\).

Write the formula for heat transfer rate

Now, we will write the heat transfer rate formula, which relates the rate of evaporation of water (mass flow rate), its specific latent heat of vaporization, and the heat transfer rate: $$Q = m \times L_v$$

Substitute the given values and solve for rate of evaporation

We know that the rate of heat transfer from the hot gases to water is \(48 \; kJ/s\) and the specific latent heat of vaporization of water is \(1940 \; kJ/kg\). Substitute these values into the formula and solve for \(m\): $$48 = m \times 1940$$ Divide both sides by \(1940\): $$m = \frac{48}{1940}$$ $$m = 0.0247 \; kg/s$$

Present the final answer

The rate of evaporation of water in the gas-fired boiler is approximately \(0.0247 \; kg/s\).