Thermal Properties of Matter

JEE Main level, single correct, medium

79 of 126

Question 79 of 126

In an experiment, a sphere of aluminium of mass 0.20kg0.20kg is heated up to 150∘C150^{\circ}C . Immediately, it is put into water of volume 150cc150ccat 27oC{27}^{o}C kept in a calorimeter of water equivalent to0.025kg0.025kg . The final temperature of the system is 40oC{40}^{o}C . The specific heat of the aluminium is(take 4.2Joule=1calorie4.2Joule=1calorie )

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Answer: (A) 434J kg−1oC434{\text{J kg}}^{-1}{ }^{o}C

Let SS be the specific heat of aluminium

QQ given = QQ used

⇒1000×0.2×S×(150−40)=150×1×(40−27)+25×1×(40−27)\Rightarrow 1000\times 0.2\times S\times (150-40)=150\times 1\times (40-27)+25\times 1\times (40-27)

⇒200×S×110=150×13+25×13\Rightarrow 200\times S\times 110=150\times 13+25\times 13

\Rightarrow S=\dfrac{13\times 175}{200\times 110}=0.1034 cal{g}^{-1} ^{\circ}C
\Rightarrow S=103.4\times 4.2J{kg}^{-1}^{\circ}C=434J{kg}^{-1}^{\circ}C

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