Kinetic Theory

JEE Main level, single correct, medium

109 of 168

Question 109 of 168

An unknown metal of mass 192g192 g heated to a temperature of 100∘C100^{\circ}C was immersed into a brass calorimeter of mass 128g128g containing 240g240 g of water at a temperature of 8.4oC.{8.4}^{o}C. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5oC.{21.5}^{o}C. (( Specific heat of brass is 394Jkg−1K−1)394J k{g}^{-1}{K}^{-1})

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Answer: (A) 916Jkg−1K−1916J k{g}^{-1}{K}^{-1}

Conservation of energy:

msΔT=(mbsb+mwsw)ΔTwms\Delta T=\left({m}_{b}{s}_{b}+{m}_{w}{s}_{w}\right)\Delta {T}_{w}

192×10−3s(100−21.5)=(128×394+240×4182)×10−3×(21.5−8.4)192\times {10}^{-3}s\left(100-21.5\right)=\left(128\times 394+240\times 4182\right)\times {10}^{-3}\times \left(21.5-8.4\right)

s=(50432+1003680)(13.1)15072=916.19≃916s=\dfrac{\left(50432+1003680\right)\left(13.1\right)}{15072}=916.19≃916 Jkg−1K−1Jk{g}^{-1}{K}^{-1}

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