Question

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 amount of heat required to raise the temperature of this block from ${20^ \circ }$ to ${80^ \circ }$ is ?
(specific heats of aluminium, brass and copper are $0.216,0.0917$ and $0.0931ca{l^{ - 1}}k{g^0}{C^{ - 1}}$ , respectively)
A. $96.2$ cal
B. $44.4$ cal
C. $86.2$ cal
D. $62.8$ cal

Answer 1

Hint:To calculate the amount of heat required to raise the temperature of the block, we make use of the concept of specific heat capacity of the substance in which the amount of heat required to raise temperature of the substance is product of mass, specific heat of substance and the temperature difference.

Formula used:
The amount of heat is given by
$Q = mc\Delta T$
Where, $m$ - mass of the substance, $c$ - specific heat of the substance and $\Delta T$ - temperature difference.

Complete step by step answer:
In the question, a single block is made from the mixture of three metals having different mass and specific heats. The temperature difference is given by,
$\Delta T = 80 - 20 = {60^ \circ }$
Now, the amount of heat required to raise the temperature is given by
$Q = {m_1}{c_1}\Delta T + {m_2}{c_2}\Delta T + {m_3}{c_3}\Delta T$
Where, ${m_1},{m_2},{m_3}$ - masses of the aluminium , brass and copper,respectively.
${c_1},{c_2},{c_3}$ - specific heats of aluminium, brass and copper,respectively.
$\Rightarrow Q = \left( {{m_1}{c_1} + {m_2}{c_2} + {m_3}{c_3}} \right)\Delta T$
Substituting the values, we get
$ Q = \left( {2.4 \times 0.216 + 1.6 \times 0.0917 + 0.8 \times 0.0931} \right)60$
$\therefore Q = \left( {0.7396} \right)60 = 44.376$
We get, \[Q = 44.4\] cal

Hence, option B is correct.

Note: The amount of heat required to change the temperature of unit mass of a substance by unity is known as specific heat capacity of the substance. It depends on the nature of the substance and its temperature. Here, the mixture of three metals is done, but their specific heat capacities are different and the rise in temperature is of the whole block.