calculate the increase in entropy when 1gm of ice at -10C is converted into steam at 100C. specific heat of ice=0.5,
The change in entropy will occur in 4 steps .
1) Increase in entropy when temp of ice changes from 263K to 273K
2)Increase in entropy when ice at 273K is transformed into water at same temp
3) Increase in entropy when 1 gm of water of 273K is changed into water at 373k
4) Increase in entropy when 1gm of water at 373K is changed into steam at same temp .
After mathematical calculations in the above mentioned 4 steps and then further adding all those four calculated values the total increase in the entropy will be .... 2.0706cals/K .
To calculate the increase in entropy when ice at -10°C is converted into steam at 100°C, we need to consider the entropy changes at each step:
Step 1: Heating the ice from -10°C to 0°C.
Step 2: Melting the ice at 0°C.
Step 3: Heating the water from 0°C to 100°C.
Step 4: Evaporating the water at 100°C.
To calculate the entropy change at each step, we can use the following formulas:
For step 1:
ΔS1 = m * Cp * ln(T2 / T1)
where:
m = mass of the ice (1 gram)
Cp = specific heat capacity of the ice (0.5)
T1 = initial temperature (-10°C or 263 K)
T2 = final temperature (0°C or 273 K)
ΔS1 = 1 * 0.5 * ln(273 / 263)
ΔS1 = 1 * 0.5 * ln(1.038)
Step 2:
ΔS2 = m * ΔHfus / T
where:
ΔHfus = heat of fusion of ice
T = melting point of ice (0°C or 273 K)
The heat of fusion of ice is typically around 333.55 J/g
ΔS2 = 1 * 333.55 / 273
Step 3:
ΔS3 = m * Cp * ln(T2 / T1)
where:
Cp = specific heat capacity of water (4.18 J/g°C)
T1 = initial temperature (0°C or 273 K)
T2 = final temperature (100°C or 373 K)
ΔS3 = 1 * 4.18 * ln(373 / 273)
Step 4:
ΔS4 = m * ΔHvap / T
where:
ΔHvap = heat of vaporization of water
T = boiling point of water (100°C or 373 K)
The heat of vaporization of water is typically around 2257 J/g
ΔS4 = 1 * 2257 / 373
Finally, to calculate the total increase in entropy, we sum up the individual entropy changes:
ΔS_total = ΔS1 + ΔS2 + ΔS3 + ΔS4
Note: The values used for specific heat capacities, heat of fusion, and heat of vaporization are approximate values and can vary slightly depending on the source.
You can plug in these values into the above formulas to calculate the increase in entropy at each step and the total increase in entropy.
To calculate the increase in entropy, we need to consider the phase changes involved in converting the ice to steam.
The first step is to calculate the entropy change during the heating of the ice from -10°C to 0°C and then melting it to form water at 0°C.
The increase in entropy during heating is given by the equation:
ΔS1 = m * c * ln(Tf / Ti)
Where:
m = mass of the ice (1 g)
c = specific heat capacity of ice (0.5 cal/g°C)
Ti = initial temperature (-10°C)
Tf = final temperature (0°C)
Substituting the given values:
ΔS1 = 1 * 0.5 * ln(0 / -10)
The natural logarithm of 0 is undefined, so we take the limit as the temperature approaches 0:
ΔS1 = 1 * 0.5 * ln(0+ / -10) = 1 * 0.5 * ln(0+ / -10)
Next, we need to calculate the entropy change during the phase change from solid (ice) to liquid (water) at 0°C. The entropy change during this phase change is given by:
ΔS2 = ΔHfusion / T
Where:
ΔHfusion = enthalpy of fusion (heat required to convert 1 g of ice to water at 0°C) = 80 cal/g
T = temperature (0°C)
Substituting the given values:
ΔS2 = 80 / 0
Again, the natural logarithm of 0 is undefined, so we take the limit as the temperature approaches 0:
ΔS2 = 80 / 0 = ∞
Finally, we need to calculate the entropy change during the heating of the water from 0°C to 100°C and then vaporizing it to form steam at 100°C.
The increase in entropy during heating is given by the equation:
ΔS3 = m * c * ln(Tf / Ti)
Where:
m = mass of the water (1 g)
c = specific heat capacity of water (1 cal/g°C)
Ti = initial temperature (0°C)
Tf = final temperature (100°C)
Substituting the given values:
ΔS3 = 1 * 1 * ln(100 / 0)
ΔS3 = 1 * 1 * ln(∞) = ∞
The total increase in entropy is the sum of the entropy changes for each step:
Total ΔS = ΔS1 + ΔS2 + ΔS3
Since ΔS2 and ΔS3 are both infinite, the total increase in entropy is also infinite when 1 g of ice at -10°C is converted into steam at 100°C.