A metal block is made from a mixture of 2.4 kg of aluminium, 1.6 kg of brass and 0.8 kg of copper. The metal…

A metal block is made from a mixture of 2.4 kg of aluminium, 1.6 kg of brass and 0.8 kg of copper. The metal block is initially at $20^{\circ} \mathrm{C}$. If the heat supplied to the metal block is 44.4 calories, find the final temperature of the block if specific heats of aluminium, brass and copper are $0.216,0.0917,0.0931 \mathrm{cal} . \mathrm{kg}^{-1} \mathrm{C}^{-1}$ respectively.
  1. $100^{\circ} \mathrm{C}$
  2. $60^{\circ} \mathrm{C}$
  3. $40^{\circ} \mathrm{C}$
  4. $80^{\circ} \mathrm{C}$

Solution

$\begin{aligned} & \text { } \mathrm{Q}=\left(\mathrm{m}_1 \mathrm{~s}_1+\mathrm{m}_2 \mathrm{~s}_2+\mathrm{m}_3 \mathrm{~s}_3\right) \Delta \mathrm{T} \\ & \Rightarrow 44.4=(2.4 \times 0.216+1.6 \times 0.0917+0.8 \times 0.0931) \Delta \mathrm{T} \\ & \Rightarrow \Delta \mathrm{T}=60 \Rightarrow \mathrm{~T}-20=60 \\ & \therefore \mathrm{~T}=80^{\circ} \mathrm{c}\end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 2)

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