Thermal Properties of Matter

JEE Main level, single correct, medium

74 of 126

Question 74 of 126

1kg1kg of water, at 20∘C20^{\circ}C is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20Ω.20 \Omega . The rms voltage in the mains is 200V200V. Ignoring heat loss from the kettle, time taken for water to evaporate fully is close to
[ Specific heat of water =4200J{kg}^{-1}^{\circ}{C}^{-1} Latent heat of water =2260kJkg−1=2260kJk{g}^{-1} ]

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Answer: (C) 22min⁡22\min

Given specific heat of the water 4200J{kg}^{-1}^{\circ}{C}^{-1}

Latent heat of the water =2260kJkg−1=2260 kJk{g}^{-1}

Q=P×tQ=P\times t

Q=mcΔT+mLQ=mc\Delta T+mL

⇒P×t=mcΔT+mL\Rightarrow P\times t=mc\Delta T+mL

⇒Vrms2R×t=mcΔT+mL\Rightarrow \dfrac{{V}_{rms}^{2}}{R}\times t=mc\Delta T+mL

⇒(200)220×t=4200×80+2260×103\Rightarrow \dfrac{{\left(200\right)}^{2}}{20}\times t=4200\times 80+2260\times {10}^{3}

⇒t=1298s≃22min\Rightarrow t=1298\text{s}≃22 min

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