Question

If the radii of the two copper sphere are in the ration $1:3$ and their temperatures are in the ratio $9:1$ then the ratio of the heat contents in them will be

• A. $1:3$
• B. $1:4$
• C. $2:1$
• D. $4:1$

Answer 1

The correct option is A $1:3$

We have the heat content as $Q=m{C}_p\Delta T$. $C_p$ is constant for a given material.

Thus, we get $\frac{Q_1}{Q_2}=\frac{m_1{T}_1}{m_2{T}_2}$.

As the volume of the sphere is given $\frac{4}{3}\pi r^3$. Thus $\frac{m_1}{m_2}=\frac{r_1^3}{r_2^3}$.
It is given that $\frac{r_1}{r_2}=\frac{1}{3}$, we get $\frac{m_1}{m_2}=\frac{1}{27}$ and also $\frac{T_1}{T_2}=9$.

Thus we get $\frac{Q_1}{Q_2}=\frac{1}{3}$