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One gram of water on evaporation at atmospheric pressure forms 1671cm3 of steam. Heat of vaporization at this pressure is 540 cal/g. Calculate the increase in the internal energy. Atmospheric pressure = 1×105N/m2.
Select one:
  • a)
    6 × 108J
  • b)
    5.3 × 102J
  • c)
    2.1 × 103J
  • d)
    20 × 106J
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
One gram of water on evaporation at atmospheric pressure forms 1671cm3...
Understanding the Problem
To calculate the increase in internal energy when 1 gram of water evaporates into steam, we need to consider the heat of vaporization and the work done by the steam against atmospheric pressure.
Given Data
- Mass of water (m) = 1 g = 0.001 kg
- Heat of vaporization (L) = 540 cal/g = 540 * 4.184 J/g = 2268 J
- Volume of steam (V) = 1671 cm³ = 0.001671 m³
- Atmospheric pressure (P) = 1 × 10^5 N/m²
Calculating Work Done
The work done (W) by the steam during evaporation can be calculated using the formula:
W = P * ΔV
Where ΔV is the change in volume. Since we start with liquid water (negligible volume) and end with steam:
- W = P * V = (1 × 10^5 N/m²) * (0.001671 m³) = 167.1 J
Applying the First Law of Thermodynamics
According to the First Law of Thermodynamics:
ΔU = Q - W
Where:
- ΔU = change in internal energy
- Q = heat added (which is the heat of vaporization)
- W = work done by the system
Substituting the values:
- Q = 2268 J (from heat of vaporization)
- W = 167.1 J
ΔU = 2268 J - 167.1 J = 2100.9 J
Final Result
Thus, the increase in internal energy when 1 gram of water evaporates is approximately:
ΔU ≈ 2.1 × 10^3 J
Hence, the correct answer is option 'C'.
Community Answer
One gram of water on evaporation at atmospheric pressure forms 1671cm3...
ΔQ = ΔW
ΔU = mL
ΔW = pΔV
ΔU = mL – pΔV
So, mL = 1 × 540 × 4.2 = 2268 J
Volume of 1gm of water = 1cm3
pΔV = 1 × 105(1671 – 1) × 10-6= 167 J
Thus, increase in internal energy is 
ΔU = 2268 – 167 = 2.1 × 103J
The correct answer is: 2.1 × 103J
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One gram of water on evaporation at atmospheric pressure forms 1671cm3 of steam. Heat of vaporization at this pressure is 540 cal/g. Calculate the increase in the internal energy. Atmospheric pressure = 1×105N/m2.Select one:a)6 × 108Jb)5.3 × 102Jc)2.1 × 103Jd)20 × 106JCorrect answer is option 'C'. Can you explain this answer?
Question Description
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