1.00 kg of liquid water at 100°C undergoes a phase change into steam at 100C∘ at 1.0 atm (take it to be 1.00×105 Pa). The initial volume of the liquid water was 1.00×10-3 m3 which is changed to 2.001 m3 of steam. Find the change in the internal energy of the system. [Use heat of vaporization ≃2000 kJ kg-1]

TS EAMCET · Physics · Thermodynamics

$1.00 kg$ of liquid water at $100 ° C$ undergoes a phase change into steam at $100 {}^{\circ}C$ at $1.0$ atm (take it to be $1.00 \times 10^{5} Pa$ ). The initial volume of the liquid water was $1.00 \times 10^{- 3} m^{3}$ which is changed to $2.001 m^{3}$ of steam. Find the change in the internal energy of the system.
[Use heat of vaporization $≃ 2000 kJ {kg}^{- 1}$ ]

A $1800 kJ$
B $200 kJ$
C $2000 kJ$
D $80 kJ$

Verified Solution

Answer & Solution

Correct Answer

(A) $1800 kJ$

Step-by-step Solution

Detailed explanation

According to the first law of thermodynamics, ∆Q=∆U+W⇒∆U=∆Q-W The heat given for the phase change of water is ∆Q=mL=2000 kJ. The change in the volume during phase change is ∆V=2.001-0.001=2 m3. Work done by the steam will be…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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