I once was given a metal whiskey flask for being in my cousin’s wedding. When it got dented, I
put in 1 gram of H2O (initially 21°C, just like the air filling the rest of the flask) and heated it up to
boil the water. It popped the dent out.
Assume the flask had a rectangular cross section, with a height of 15 cm, a width of 10 cm, and a
thickness of 2 cm. Assume that in order to pop the dent out, an outward pressure difference of
1.0E6 Pa was required (that is, the outward pressure on the flask minus the inward pressure on
the flask was 1.0E6 Pa). How much heat had to be added to the contents of the flask?
At the instant the dent popped out, was the gas inside the flask doing positive work, or was
positive work being done to the gas?
To calculate the amount of heat that had to be added to the contents of the flask, we can use the equation:
Q = m * c * ΔT
Where:
Q = amount of heat transferred
m = mass of the water
c = specific heat capacity of water
ΔT = change in temperature of the water
First, let's calculate the mass of the water. The density of water is approximately 1 gram/cm^3. Since we added 1 gram of water, the volume of water in the flask is also 1 cm^3, which is equal to 1 mL. As 1 mL of water is equal to 1 gram, the mass of water is 1 gram.
Next, the specific heat capacity of water is approximately 4.18 J/g°C.
Given that the initial temperature of the water and air is 21°C, and the boiling point of water is 100°C, we can calculate the change in temperature:
ΔT = 100°C - 21°C
ΔT = 79°C
Now we can plug the values into the equation to calculate the amount of heat required:
Q = (1 g) * (4.18 J/g°C) * (79°C)
Q ≈ 331 J
Therefore, approximately 331 Joules of heat had to be added to the contents of the flask to pop out the dent.
At the instant the dent popped out, the gas inside the flask was doing positive work. This is because when the water is heated and converted to steam, it expands, creating an outward pressure on the flask. The gas does work on the surrounding environment by pushing against the inward pressure, resulting in the dent popping out.
To calculate the amount of heat required to pop out the dent on the flask and determine whether the gas inside the flask is doing positive work or work is being done to the gas, we need to consider the pressure and temperature changes.
First, let's calculate the change in volume of the flask due to the dent. The flask has a rectangular cross-section with dimensions:
- Height (h) = 15 cm
- Width (w) = 10 cm
- Thickness (t) = 2 cm
The change in volume (ΔV) caused by the dent can be calculated as the difference in volume before and after denting:
ΔV = h * w * t
Next, we need to calculate the change in pressure (ΔP) required to pop out the dent. The given information states that the outward pressure difference was 1.0E6 Pa.
Now, let's determine the work done. The work done on a gas can be calculated as the product of pressure change and volume change:
Work done = ΔP * ΔV
If the work done is positive, then the gas is doing positive work. If the work done is negative, then positive work is being done on the gas.
To calculate the amount of heat added to the contents of the flask, we need to consider the change in temperature of the water. The specific heat capacity of water is approximately 4.18 J/g°C.
Finally, we can calculate the amount of heat added (Q) using the formula:
Q = m * c * ΔT
Where:
- Q is the heat added
- m is the mass of the water (1 gram)
- c is the specific heat capacity of water (4.18 J/g°C)
- ΔT is the change in temperature from the initial temperature (21°C) to boiling point (100°C)
By substituting the given values into the formulas, you can find the amount of heat added to the flask and determine whether the gas inside the flask is doing positive work or having work done on it.