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NEET PHYSICSThermodynamicsMedium

Question

1 g of water of volume 1 cm31 \text{ cm}^3 at 100C100^{\circ}\text{C} is converted into steam at the same temperature under normal atmospheric pressure 1×105 Pa\approx 1 \times 10^5 \text{ Pa}. The volume of steam formed equals 1671 cm31671 \text{ cm}^3. If the specific latent heat of vaporization of water is 2256 J/g2256 \text{ J/g}, the change in internal energy is:

A

2423 J

B

2089 J

C

167 J

D

2256 J

Step-by-Step Solution

According to the First Law of Thermodynamics, the change in internal energy (ΔU\Delta U) is given by: ΔQ=ΔU+ΔW    ΔU=ΔQΔW\Delta Q = \Delta U + \Delta W \implies \Delta U = \Delta Q - \Delta W

  1. Calculate Heat Absorbed (ΔQ\Delta Q): The heat absorbed during the phase change is determined by the specific latent heat of vaporization (LL) and the mass (mm). ΔQ=m×L\Delta Q = m \times L ΔQ=1 g×2256 J/g=2256 J\Delta Q = 1 \text{ g} \times 2256 \text{ J/g} = 2256 \text{ J}

  2. Calculate Work Done (ΔW\Delta W): Work done during expansion at constant pressure is given by ΔW=PΔV\Delta W = P\Delta V. Pressure (PP) = 1×105 Pa1 \times 10^5 \text{ Pa} Change in volume (ΔV\Delta V) = VsteamVwater=1671 cm31 cm3=1670 cm3V_{\text{steam}} - V_{\text{water}} = 1671 \text{ cm}^3 - 1 \text{ cm}^3 = 1670 \text{ cm}^3

  • Convert ΔV\Delta V to SI units (textm3\\text{m}^3): 1670×106 m31670 \times 10^{-6} \text{ m}^3

ΔW=(1×105 Pa)×(1670×106 m3)=167 J\Delta W = (1 \times 10^5 \text{ Pa}) \times (1670 \times 10^{-6} \text{ m}^3) = 167 \text{ J}

  1. Calculate Internal Energy Change (ΔU\Delta U): ΔU=2256 J167 J=2089 J\Delta U = 2256 \text{ J} - 167 \text{ J} = 2089 \text{ J}

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Thermodynamics. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSThermodynamicsvolumecirctextcconvertedtemperaturenormal

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