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The variation of saturation pressure with saturation temperature for a liquid is 0.1 bar/K at 400 K. The specific volume of saturated liquid and dry saturated vapour at 400 K are 0.251 and 0.001 m3/kg. What will be value of latent heat of vaporization using Clausius clapeyron equation?
  • a)
    16000 kJ/kg
  • b)
    1600 kJ/kg
  • c)
    1000 kJ/kg
  • d)
    160 kK/kg
Correct answer is option 'C'. Can you explain this answer?
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Given data:
Saturation temperature (T) = 400 K
Variation of saturation pressure with saturation temperature (dp/dT) = 0.1 bar/K
Specific volume of saturated liquid (vf) = 0.251 m³/kg
Specific volume of dry saturated vapor (vg) = 0.001 m³/kg

Formula:
The Clausius-Clapeyron equation is given by:
ln(P2/P1) = (ΔHvap/R)(1/T1 - 1/T2)
Where,
P1 and P2 are the initial and final saturation pressures,
T1 and T2 are the initial and final saturation temperatures,
ΔHvap is the latent heat of vaporization, and
R is the specific gas constant.

Calculation:
We are given the variation of saturation pressure with saturation temperature (dp/dT) = 0.1 bar/K. This means that for every 1 K increase in temperature, the pressure increases by 0.1 bar.

To find the latent heat of vaporization (ΔHvap), we need to find the difference in saturation pressures (ΔP) and saturation temperatures (ΔT) between the liquid and vapor states.

ΔP = P2 - P1
ΔT = T2 - T1

Using the given data, we can calculate the values of P1, P2, T1, and T2:

P1 = saturation pressure at T1 = P2 - dp/dT * ΔT
P2 = saturation pressure at T2 = P1 + dp/dT * ΔT
T1 = 400 K
T2 = 400 K

Substituting these values into the Clausius-Clapeyron equation, we have:

ln((P2 - dp/dT * ΔT)/P1) = (ΔHvap/R)(1/T1 - 1/T2)

Simplifying the equation, we get:

ΔHvap/R = (1/T1 - 1/T2) * ln((P2 - dp/dT * ΔT)/P1)

Since R is the specific gas constant, we can assume its value to be constant.

Now, we can substitute the known values into the equation and calculate ΔHvap:

ΔHvap = R * (1/T1 - 1/T2) * ln((P2 - dp/dT * ΔT)/P1)

Using the given specific gas constant and the calculated values of ΔT, P1, and P2, we can solve for ΔHvap:

ΔHvap = (8.314 J/mol K) * (1/400 K - 1/400 K) * ln((P2 - 0.1 bar/K * 0 K)/P1)

Converting the result from J/mol to kJ/kg, we find that the value of ΔHvap is approximately 1000 kJ/kg.

Therefore, the correct answer is option C) 1000 kJ/kg.
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The variation of saturation pressure with saturation temperature for a liquid is 0.1 bar/K at 400 K. The specific volume of saturated liquid and dry saturated vapour at 400 K are 0.251 and 0.001 m3/kg. What will be value of latentheat of vaporization using Clausius clapeyron equation?a)16000 kJ/kgb)1600 kJ/kgc)1000 kJ/kgd)160 kK/kgCorrect answer is option 'C'. Can you explain this answer?
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