Question

If a leaf is to maintain a temperature of \(40^{\circ} \mathrm{C}\) (reasonable for a leaf), it must lose \(250 \mathrm{W} / \mathrm{m}^{2}\) by transpiration (evaporative heat loss). Note that the leaf also loses heat by radiation, but we will neglect this. How much water is lost after 1 h through transpiration only? The area of the leaf is \(0.005 \mathrm{m}^{2}\).

Short answer

Answer: 0.002 liters

Step-by-step solution

Identify the given information and the missing variable

We are given: - Heat loss through transpiration: 250 W/m² - Temperature to maintain: 40°C - Area of the leaf: 0.005 m² We need to find the mass of water lost after 1 hour.

Calculate the total heat loss through transpiration

To find the total heat loss, we multiply the heat loss per square meter by the area of the leaf: Total heat loss = Heat loss per square meter × Area of the leaf Total heat loss = 250 W/m² × 0.005 m² = 1.25 W

Calculate the energy lost after 1 hour of transpiration

To calculate the total energy lost, we multiply the total heat loss by the time in seconds (1 hour = 3600 seconds): Energy lost = Total heat loss × Time Energy lost = 1.25 W × 3600 s = 4500 J

Use the latent heat of vaporization to find the mass of water lost

The latent heat of vaporization of water is 2.25 x 10^6 J/kg. To find the mass of water lost, we use the following formula: Mass of water lost = Energy lost / Latent heat of vaporization Mass of water lost = 4500 J / (2.25 × 10^6 J/kg) = 0.002 kg

Convert the mass of water into liters

To convert the mass of water lost into liters, we use the density of water (1 kg/L): Water lost (in liters) = Mass of water lost / Density of water Water lost (in liters) = 0.002 kg / 1 kg/L = 0.002 L So, after 1 hour of transpiration, the leaf loses 0.002 liters of water.