calculate the amount of heat released when 50g of water at 100degrees hits the skin, condenses, cools the body to 37 degrees
mc(delta)T
50x1(100-37)
=3,150
3150
To calculate the amount of heat released, we need to consider the following steps:
Step 1: Calculate the heat released when cooling from 100°C to 37°C.
Step 2: Calculate the heat released when condensing from a gas state to a liquid state.
Step 3: Sum the heat released in both steps to get the total heat released.
Step 1: Heat released when cooling from 100°C to 37°C
The specific heat capacity of water is \(4.18 \, \text{J/g°C}\).
The formula to calculate the heat released during cooling is:
\(Q = m \cdot c \cdot \Delta T\),
where:
Q = heat released (in Joules),
m = mass of water (in grams),
c = specific heat capacity of water (in J/g°C),
\(\Delta T\) = change in temperature (in °C).
Using the given values:
m = 50g,
c = 4.18 J/g°C,
\(\Delta T = 100°C - 37°C = 63°C\),
\(Q_1 = 50g \cdot 4.18J/g°C \cdot 63°C\)
Calculate \(Q_1\) to find the heat released when cooling.
Step 2: Heat released when condensing from a gas state to a liquid state
The heat of vaporization for water is \(40.7 \, \text{kJ/mol}\), which can be converted to \(40.7 \, \text{J/g}\).
Using the given mass of water, m = 50g,
\(Q_2 = 50g \cdot 40.7J/g\)
Calculate \(Q_2\) to find the heat released when condensing.
Step 3: Calculate the total heat released:
The total heat released is the sum of \(Q_1\) and \(Q_2\).
\(Q_{\text{total}} = Q_1 + Q_2\)
Calculate \(Q_{\text{total}}\) to find the total heat released.
Please note that in this calculation, we assume that there is no heat loss to the surroundings.
To calculate the amount of heat released, we need to consider the following steps:
1. Determine the heat required to cool the water from its initial temperature of 100 degrees Celsius to 37 degrees Celsius.
2. Calculate the heat released during condensation as the water vapor turns into liquid water on contact with the skin.
Step 1: Heat required to cool the water
The formula to calculate the heat (Q) required to change the temperature of a substance is:
Q = mass × specific heat capacity × temperature change
The specific heat capacity of water is approximately 4.18 J/g°C.
Q = 50g × 4.18 J/g°C × (100°C - 37°C)
Q = 50g × 4.18 J/g°C × 63°C
Q ≈ 13230 J (rounded to the nearest whole number)
Step 2: Heat released during condensation
During condensation, the water vapor releases a certain amount of energy to cool down and turn into liquid water. This energy is called the latent heat of vaporization.
The latent heat of vaporization for water is approximately 2260 J/g.
The amount of water vapor produced can be calculated using the equation:
Amount of water vapor = mass of water / molar mass of water = 50g / 18 g/mol ≈ 2.78 mol
The heat released during condensation is given by:
Q = amount of water vapor × latent heat of vaporization
Q = 2.78 mol × 2260 J/mol
Q ≈ 6282.8 J (rounded to the nearest whole number)
Finally, to find the total heat released, we add the heat required to cool the water and the heat released during condensation:
Total heat released = heat required to cool the water + heat released during condensation
Total heat released ≈ 13230 J + 6282.8 J
Total heat released ≈ 19512.8 J
Therefore, approximately 19512.8 J of heat are released when 50g of water at 100 degrees Celsius hits the skin, condenses, and cools the body to 37 degrees Celsius.