Question

The specific heat capacity of a metal is $0.01{\text{cal/g}}^{\circ }\text{C}$. If heat capacity of $m\text{kg}$ of metal is $0.42\text{J}{/}^{\circ }\text{C}$. Find the value of $m$.

• A. ${10}^{-2}$
• B. ${10}^{-1}$
• C. $1$
• D. ${10}^{-3}$

Answer 1

The correct option is A ${10}^{-2}$

Specific heat capacity $\left(c\right)=0.01{\text{cal/g}}^{\circ }\text{C}$
Heat capacity $\left(C\right)=0.42\text{J}{/}^{\circ }\text{C}$
We know;
Specific heat capacity $\left(c\right)=0.01{\text{cal/g}}^{\circ }\text{C}=\frac{0.01\times 4.2}{{10}^{-3}}{\text{J/kg}}^{\circ }\text{C}$
$=42{\text{J/kg}}^{\circ }\text{C}$
Also,
Heat capacity $\left(C\right)=m\times 42{\text{J/kg}}^{\circ }\text{C}\Rightarrow 0.42{\text{J/}}^{\circ }\text{C}=m\times 42{\text{J/kg}}^{\circ }\text{C}$
$\Rightarrow m={10}^{-2}\text{kg}$