Thermal Properties of Matter

JEE Main level, single correct, medium

80 of 126

Question 80 of 126

A copper ball of mass 100g100 \text{g} is at a temperature TT. It is dropped in a copper calorimeter of mass 100g,100 \text{g,} filled with 170g170 \text{g} of water at room temperature. Subsequently, the temperature of the system is found to be 75∘C75^{\circ}C. TT is given by:
(Given: room temperature =30∘C=30^{\circ}C, specific heat of copper =0.1cal{g}^{-1}^{\circ}{C}^{-1})

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Answer: (C) 885∘C885^{\circ}C

mcb=100g,(ToC)mc=100g,(30oC)mw=170g,(30oC)\begin{matrix}{m}_{cb}=100g, & & \left({T}^{o}C\right) \\ {m}_{c}=100g, & & \left({30}^{o}C\right) \\ {m}_{w}=170g, & & \left({30}^{o}C\right)\end{matrix}

Net heat loss = Net heat gain

⇒100×0.1×(T−75)=100×0.1×(75−30)+170×1×(75−30)\Rightarrow 100\times 0.1\times \left(T-75\right)=100\times 0.1\times \left(75-30\right)+170\times 1\times \left(75-30\right)

⇒T−75=45+17×45\Rightarrow T-75=45+17\times 45

⇒T=885∘C\Rightarrow T=885^{\circ}C.

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