In an experiment a sphere of aluminium of mass 0.20 kg is heated upto $150^{\circ} \mathrm{C}$. Imme

Question

In an experiment a sphere of aluminium of mass 0.20 kg is heated upto $150^{\circ} \mathrm{C}$. Immediately, it is put into water of volume 150 cc at $27^{\circ} \mathrm{C}$ kept in a calorimeter of water equivalent to 0.025 kg . Final temperature of the system is $40^{\circ} \mathrm{C}$. The specific heat of aluminium is (take 4.2 joule $=1$ calorie)\

Professor PC Thomas Classes · Answer

(d) : Let $S$ be the specific heat of aluminium.\ By principle of calorimetry, $Q_{	ext {Given }}=Q_{	ext {used }}$\ Heat capacity of water $=1 \mathrm{cal} / \mathrm{g}-{ }^{\circ} \mathrm{C}$\ $200 	imes S 	imes(150-40)=150 	imes 1 	imes 1 	imes(40-27)$\ $+25 	imes 1 	imes(40-27) 200 	imes S 	imes 110$\ $=150 	imes 13+25 	imes 13$\ $S=\frac{13 	imes 175}{200 	imes 110}=0.1034 \mathrm{cal} / \mathrm{g}-{ }^{\circ} \mathrm{C}$\ $=103.4 	imes 4.2 \mathrm{~J} / \mathrm{kg}-{ }^{\circ} \mathrm{C}=434 \mathrm{~J} / \mathrm{kg}-{ }^{\circ} \mathrm{C}$\