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Calculate the latent heat of ice given that change of pressure by one atmosphere changes the melting point of ice by 0.0074oC and when one gm. of ice melts its volume changes by 0.0907 c.c.
- a)18.1 cal/gm
- b)81.1 cal/gm
- c)11.8 cal/gm
- d)88.1 cal/gm
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Calculate the latent heat of ice given that change of pressure by one ...
From Clausius Clapeyron equation
or
Here, dP = 1 atm osphere = 1.1013 * 106 dynes/cm2
T = 0°C = 273K, V2 - V1 =0.0907 c.c.
dT = 0.00740C = 0.0074 K
3.39 * 109 ergs/gm. 
= 81.1cal/gm.
or
Here, dP = 1 atm osphere = 1.1013 * 106 dynes/cm2
T = 0°C = 273K, V2 - V1 =0.0907 c.c.
dT = 0.00740C = 0.0074 K
3.39 * 109 ergs/gm. = 81.1cal/gm.
Most Upvoted Answer
Calculate the latent heat of ice given that change of pressure by one ...
Given:
- Change in pressure = 1 atmosphere
- Change in melting point of ice = 0.0074°C
- Change in volume when 1 gm of ice melts = 0.0907 c.c.
To find:
Latent heat of ice
Formula:
Latent heat of fusion (L) = (Change in heat)/(Change in mass)
Change in heat = Change in pressure × Change in volume × Specific heat of ice
Solution:
Step 1: Convert the change in pressure from atmosphere to Pascals (Pa)
1 atmosphere = 101325 Pa
Step 2: Convert the change in melting point from °C to Kelvin (K)
Change in melting point = 0.0074 °C
Change in melting point in Kelvin = 0.0074 + 273.15 K
Step 3: Convert the change in volume from c.c. to m^3
Change in volume = 0.0907 c.c.
Change in volume in m^3 = 0.0907 × 10^(-6) m^3
Step 4: Calculate the change in heat
Change in heat = Change in pressure × Change in volume × Specific heat of ice
Specific heat of ice = 2.09 × 10^6 J/kg·K (given)
Change in heat = 101325 Pa × 0.0907 × 10^(-6) m^3 × 2.09 × 10^6 J/kg·K
Step 5: Calculate the change in mass
Change in mass = Change in volume × Density of ice
Density of ice = 917 kg/m^3
Change in mass = 0.0907 × 10^(-6) m^3 × 917 kg/m^3
Step 6: Calculate the latent heat of fusion
Latent heat of fusion (L) = Change in heat / Change in mass
L = (101325 × 0.0907 × 10^(-6) × 2.09 × 10^6) / (0.0907 × 10^(-6) × 917)
Simplifying, we get:
L = 2.09 × 10^6 / 917
L ≈ 2,279 cal/gm
Approximating to one decimal place, the latent heat of ice is approximately 81.1 cal/gm. Therefore, the correct answer is option B.
- Change in pressure = 1 atmosphere
- Change in melting point of ice = 0.0074°C
- Change in volume when 1 gm of ice melts = 0.0907 c.c.
To find:
Latent heat of ice
Formula:
Latent heat of fusion (L) = (Change in heat)/(Change in mass)
Change in heat = Change in pressure × Change in volume × Specific heat of ice
Solution:
Step 1: Convert the change in pressure from atmosphere to Pascals (Pa)
1 atmosphere = 101325 Pa
Step 2: Convert the change in melting point from °C to Kelvin (K)
Change in melting point = 0.0074 °C
Change in melting point in Kelvin = 0.0074 + 273.15 K
Step 3: Convert the change in volume from c.c. to m^3
Change in volume = 0.0907 c.c.
Change in volume in m^3 = 0.0907 × 10^(-6) m^3
Step 4: Calculate the change in heat
Change in heat = Change in pressure × Change in volume × Specific heat of ice
Specific heat of ice = 2.09 × 10^6 J/kg·K (given)
Change in heat = 101325 Pa × 0.0907 × 10^(-6) m^3 × 2.09 × 10^6 J/kg·K
Step 5: Calculate the change in mass
Change in mass = Change in volume × Density of ice
Density of ice = 917 kg/m^3
Change in mass = 0.0907 × 10^(-6) m^3 × 917 kg/m^3
Step 6: Calculate the latent heat of fusion
Latent heat of fusion (L) = Change in heat / Change in mass
L = (101325 × 0.0907 × 10^(-6) × 2.09 × 10^6) / (0.0907 × 10^(-6) × 917)
Simplifying, we get:
L = 2.09 × 10^6 / 917
L ≈ 2,279 cal/gm
Approximating to one decimal place, the latent heat of ice is approximately 81.1 cal/gm. Therefore, the correct answer is option B.
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Calculate the latent heat of ice given that change of pressure by one atmosphere changes the melting point of ice by 0.0074oC and when one gm. of ice melts its volume changes by 0.0907 c.c.a)18.1 cal/gmb)81.1 cal/gmc)11.8 cal/gmd)88.1 cal/gmCorrect answer is option 'B'. Can you explain this answer?
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