A copper ball of mass 100 gm is at a temperature T . It is dropped in a copper calorimeter of mass 1

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10-1.Thermometry, Thermal Expansion and Calorimetry

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A copper ball of mass $100\ gm$ is at a temperature $T$. It is dropped in a copper calorimeter of mass $100\ gm$, filled with $170\ gm$ of water at room temperature. Subsequently, the temperature of the system is found to be $75^o C$. $T$ is given by......$^oC$ (Given : room temperature $= 30^o C$, specific heat of copper $=$ $0.1$ $cal/gm^o C$)

A

$800$

B

$885$

C

$1250 $

D

$825$

(JEE MAIN-2017)

Solution

$Heat\,lost\,by\,copper\,ball=heat\,gained\,by\,copper\,calorimeter\,and\,water.$

$\therefore m{s_{Cu}}\left( {T – {T_f}} \right) = {m_{Cu}} \times {s_{Cu}}\left( {{T_f} – {T_0}} \right) + $

${m_w}{s_w}\left( {{T_f} – {T_0}} \right)$

$or\,100 \times 0.1 \times \left[ {T – 75} \right] = 100 \times 0.1\left( {75 – 30} \right) + $

$170 \times 1\left( {75 – 30} \right)$

$10T – 750 = 450 + 750$

$10T = 750 + 450 + 7650 = 8850$

$T = {885^ \circ }C$

Standard 11

Physics

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