A cylinder with a moveable piston contains 0.2 kg of water at 100 ºC.
The density of the water ρw
=1000 kg/m3 and that of steam is ρs
=0.6
kg/m3
. The Latent heat of vaporization of water is Lv
=2.26x106 J/kg.
Determine the change in internal energy of the water when it is
converted to steam at 100 ºC at a constant pressure of 1.0087 x 105
Pa
To determine the change in internal energy of the water when it is converted to steam at 100ºC and a constant pressure of 1.0087 x 10^5 Pa, we can use the formula:
ΔU = m * Lv
where ΔU is the change in internal energy, m is the mass of the water, and Lv is the latent heat of vaporization.
Given:
m = 0.2 kg
Lv = 2.26 x 10^6 J/kg
Using the formula, we can calculate:
ΔU = 0.2 kg * 2.26 x 10^6 J/kg
ΔU = 452,000 J
Therefore, the change in internal energy of the water when it is converted to steam at 100ºC and a constant pressure of 1.0087 x 10^5 Pa is 452,000 J.
To determine the change in internal energy of the water when it is converted to steam at 100 ºC at a constant pressure of 1.0087 x 105 Pa, we can use the formula:
ΔU = ΔQ - ΔW
where ΔU is the change in internal energy, ΔQ is the heat added to the system, and ΔW is the work done on the system.
First, let's calculate the heat added to the system. The heat added is equal to the latent heat of vaporization, multiplied by the mass of water:
ΔQ = m * Lv
Given:
m = 0.2 kg (mass of water)
Lv = 2.26 x 10^6 J/kg (latent heat of vaporization)
ΔQ = 0.2 kg * 2.26 x 10^6 J/kg
ΔQ = 452,000 J
Next, let's determine the work done on the system. Since the pressure is constant, we can use the formula:
ΔW = P * ΔV
where P is the pressure and ΔV is the change in volume.
To calculate the change in volume, we need to determine the initial and final volumes. The initial volume is the volume of the water, and the final volume is the volume of the steam. The volume of the water can be calculated using the formula:
Vw = m / ρw
Given:
ρw = 1000 kg/m3 (density of water)
Vw = 0.2 kg / 1000 kg/m3
Vw = 0.0002 m3
Since the water is being converted to steam, the final volume will be larger. The final volume can be calculated using the formula:
Vs = m / ρs
Given:
ρs = 0.6 kg/m3 (density of steam)
Vs = 0.2 kg / 0.6 kg/m3
Vs = 0.3333 m3
Now we can calculate the change in volume:
ΔV = Vs - Vw
ΔV = 0.3333 m3 - 0.0002 m3
ΔV = 0.3331 m3
Finally, we can calculate the work done on the system:
ΔW = P * ΔV
Given:
P = 1.0087 x 105 Pa (pressure)
ΔW = 1.0087 x 105 Pa * 0.3331 m3
ΔW = 33,663.97 J
Now we can calculate the change in internal energy using the formula:
ΔU = ΔQ - ΔW
ΔU = 452,000 J - 33,663.97 J
ΔU = 418,336.03 J
Therefore, the change in internal energy of the water when it is converted to steam at 100 ºC at a constant pressure of 1.0087 x 105 Pa is 418,336.03 J.