Textbook Question
An iron boiler of mass 180 kg contains 710 kg of water at 18°C. A heater supplies energy at the rate of 58,000 kJ/h. How long does it take for the water to all have changed to steam?
313
views
20. Heat and Temperature
Latent Heat & Phase Changes
4:02 minutesProblem 41
Textbook Question
When air is inhaled, it quickly becomes saturated with water vapor as it passes through the moist airways. Consequently, an adult human exhales about 25 mg of evaporated water with each breath. Evaporation—a phase change—requires heat, and the heat energy is removed from your body. Evaporation is much like boiling, only water's heat of vaporization at 35°C is a somewhat larger 24×105 J/kg because at lower temperatures more energy is required to break the molecular bonds. At 12 breaths/min, on a dry day when the inhaled air has almost no water content, what is the body's rate of energy loss (in J/s) due to exhaled water? (For comparison, the energy loss from radiation, usually the largest loss on a cool day, is about 100 J/s.)
Verified step by step guidance1
Step 1: Identify the given values in the problem. The heat of vaporization of water at 35°C is 24×10^5 J/kg, the mass of water exhaled per breath is 25 mg (which is equivalent to 25×10^-6 kg), and the breathing rate is 12 breaths per minute.
Step 2: Convert the breathing rate from breaths per minute to breaths per second. Since there are 60 seconds in a minute, divide the breathing rate by 60: \( \text{Breaths per second} = \frac{12}{60} \).
Step 3: Calculate the energy loss per breath due to evaporation. Use the formula \( Q = m \cdot L \), where \( m \) is the mass of water exhaled per breath and \( L \) is the heat of vaporization. Substitute \( m = 25 \times 10^{-6} \, \text{kg} \) and \( L = 24 \times 10^5 \; \text{J/kg} \).
Step 4: Determine the total energy loss rate (in J/s) by multiplying the energy loss per breath by the breathing rate in breaths per second. Use the formula \( \text{Energy loss rate} = \text{Energy per breath} \times \text{Breaths per second} \).
Step 5: Compare the calculated energy loss rate due to evaporation with the given energy loss rate from radiation (100 J/s) to understand the relative significance of evaporation in the body's energy balance.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
4mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Evaporation and Heat of Vaporization
Evaporation is the process by which liquid water transforms into vapor, requiring energy to break intermolecular bonds. The heat of vaporization is the amount of energy needed to convert a unit mass of liquid into vapor without a change in temperature. At 35°C, this value is approximately 24×10^5 J/kg, indicating that significant energy is absorbed during this phase change, which contributes to cooling effects in biological systems.
Recommended video:
Guided course
05:
Finding Amount of Water Vaporized
Breathing Rate and Water Loss
The breathing rate, measured in breaths per minute, directly influences the amount of water vapor exhaled and, consequently, the energy lost through evaporation. In this scenario, an adult exhales about 25 mg of water with each breath. By calculating the total water loss over a specified time frame, one can determine the overall energy loss due to the evaporation of this water, which is critical for understanding thermoregulation in humans.
Recommended video:
Guided course
03:36Heating Cup of Water
Energy Loss Calculation
To find the body's rate of energy loss due to exhaled water, one must multiply the mass of water lost per breath by the heat of vaporization and the number of breaths taken per second. This calculation provides the energy loss in joules per second (J/s), allowing for a comparison with other forms of energy loss, such as radiation. Understanding this calculation is essential for evaluating the body's thermal balance and energy expenditure.
Recommended video:
Guided course
05:01Calculating Max Height with Energy Conservation
1:40mWatch next
Master Latent Heat & Phase Changes with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice