Question

The mass of copper is $0.120kg$ . If the specific heat capacity is $100cal{g}^{-1}°C^{-1}$^, then the thermal capacity in SI unit is

• A. $120cal$
• B. $50.4kJ$
• C. $12J$
• D. $50.4cal$

Answer 1

The correct option is B

$50.4kJ$

Step 1: Given

Mass, m =$0.120kg$

Specific heat capacity, c =$100cal{g}^{-1}°C^{-1}$

Step 2: Convert the specific heat from C G S unit to S I unit

$$\begin{gathered} \because 1cal=4.2J \\ Ig=0.001kg \\ \therefore 1cal{g}^{-1}°C^{-1}=\frac{4.2J}{0.001kg°C} \\ =4200Jk{g}^{-1}°C^{-1} \end{gathered}$$

Now calculate for $100cal{g}^{-1}°C^{-1}$

$$\begin{gathered} 100cal{g}^{-1}°C^{-1}=\left(4200\times 100\right)Jk{g}^{-1}°C^{-1} \\ =420000Jk{g}^{-1}°C^{-1} \end{gathered}$$

Step 3 - Calculate the thermal capacity

Thermal capacity is defined as The thermal capacity of a body is the heat necessary to raise the temperature of the body by one degree.”

Thermal capacity = mass of body $\times$ specific heat.

Substituting the values

$$\begin{gathered} Thermalcapacity=m\times c \\ =0.120\times 420000 \\ =50,400J \\ =50.4kJ \end{gathered}$$

Hence, the thermal capacity of 0.120 kg copper in S I unit is $50.4kJ$

Hence option B is correct.