Question

Specific heat of aluminum is $0.25cal/{g^ \circ }C$ . The water equivalent of an aluminum vessel of mass one kilogram is
$\left( A \right){\text{ 40gm}}$
$\left( B \right){\text{ 250gm}}$
$\left( C \right){\text{ 25gm}}$
$\left( D \right){\text{ 2}}{\text{.5gm}}$

Answer 1

As we know that the equivalent water will be equal to the product of the mass and the specific heat of aluminum. So by using this we will have the equation and then substituting the values, and solving it we will get the answer to this question.

Formula used
Water equivalent of the calorimeter,
$Water{\text{ equivalent = mass }} \times {\text{ specific heat}}$.

Complete step by step answer:
Here in this question, we have the values given as the specific heat of aluminum is $0.25cal/{g^ \circ }C$ .
Since heat capacity for $1kg$ of aluminum will be equal to
$\Rightarrow 1000 \times 0.25{\text{ cal}}{{\text{/}}^ \circ }C$
So on solving the above equation, we will get the value as
$\Rightarrow 250{\text{ cal}}{{\text{/}}^ \circ }C$
Now by using the formula, the water equivalent to heat capacity will be calculated as
$\Rightarrow {m_w} \times {C_w} = 250$
Now on substituting the known values, we will get the equation as
$\Rightarrow {m_w} \times 1 = 250$
And on solving it, we get
$\Rightarrow {m_w} = 250gm$
Therefore, the water equivalent of an aluminum vessel of mass one kilogram is $250gm$ .
Hence, the option $\left( b \right)$ is correct.

Note:
Specific heat can be defined as the amount of heat per unit mass that is required to raise the temperature by one degree Celsius is known to be the specific heat. The specific heat of the water will be given by $1c/g{m^ \circ }C$ . And its unit will be given by kelvin.