Calculate the pressure (in atmospheres) required to make water freeze ...
Given dT = 1
0C . V
2 - V
1 = -0.091 c.c.
L = 80 cal. = 80 * 4.2 * 10
7 ergs, T = 0 + 273 = 273 K
Applying Clapeyrons latent heat equation
or
dynes/cm
2.
= 135.2 Atmos.
Hence to lower the melting of ice by 1°C, the pressure must be raised by 135.2 atmospheres.
Now melting point of ice at atmospheric pressure is 0°C. Hence pressure required to make ice freeze at - 1 °C
= 135.2 + 1 = 136.2 atmospheres
View all questions of this test
Calculate the pressure (in atmospheres) required to make water freeze ...
Given:
- Change in specific volume when 1 gm of water freezes into ice = 0.091 cc
- Latent heat of ice = 80 cal/gm
- J = 4.2 x 10^7 ergs/cal
- 1 atmosphere = 10^6 dynes/cm^2
To find:
Pressure required to make water freeze at -10°C in atmospheres
Solution:
Step 1: Convert the change in specific volume from cc to cm^3
Given change in specific volume = 0.091 cc
1 cc = 1 cm^3
Therefore, change in specific volume = 0.091 cm^3
Step 2: Convert the latent heat of ice from calories to ergs
Given latent heat of ice = 80 cal/gm
1 cal = 4.2 x 10^7 ergs
Therefore, latent heat of ice = 80 x 4.2 x 10^7 ergs
Step 3: Calculate the pressure required to make water freeze at -10°C
The change in specific volume when water freezes into ice is given by the equation:
ΔV = Vf - Vi
Where:
ΔV = change in specific volume
Vf = final specific volume of ice
Vi = initial specific volume of water
Given ΔV = 0.091 cm^3
Let's assume the initial specific volume of water (Vi) = Vw
The final specific volume of ice (Vf) = Vi + 0.091 cm^3
The work done during the expansion of water freezing into ice is given by the equation:
W = PΔV
Where:
W = work done
P = pressure
ΔV = change in specific volume
The work done is equal to the change in internal energy (U) of the system. Therefore,
U = W = PΔV
The change in internal energy is given by the equation:
U = Q - W
Where:
U = change in internal energy
Q = heat absorbed by the system
W = work done by the system
Since the water is freezing, the heat absorbed by the system (Q) is equal to the latent heat of ice (L). Therefore,
U = L - PΔV
Since the process is reversible, we can write:
U = TΔS
Where:
T = temperature in Kelvin
ΔS = change in entropy
The change in entropy is given by the equation:
ΔS = ΔQ / T
Since the process is isothermal, ΔQ = Q = L. Therefore,
ΔS = L / T
Substituting the values of U and ΔS, we get:
L / T = L - PΔV
PΔV = L - L / T
Simplifying the equation, we get:
P = (L - L / T) / ΔV
Substituting the given values, we get:
P = (80 x 4.2 x 10^7 - 80 x 4.2 x 10^7 / T) / 0.091
Step 4: Convert the temperature from Celsius to Kelvin
Given temperature = -10°C
Calculate the pressure (in atmospheres) required to make water freeze ...
Given dT = 1
0C . V
2 - V
1 = -0.091 c.c.
L = 80 cal. = 80 * 4.2 * 10
7 ergs, T = 0 + 273 = 273 K
Applying Clapeyrons latent heat equation
or
dynes/cm
2.
= 135.2 Atmos.
Hence to lower the melting of ice by 1°C, the pressure must be raised by 135.2 atmospheres.
Now melting point of ice at atmospheric pressure is 0°C. Hence pressure required to make ice freeze at - 1 °C
= 135.2 + 1 = 136.2 atmospheres