Question

I place two substances, $1$ and $2$, in contact with each other so that they exchange heat with each other only, until they come to the same temperature. The mass of substance $1$ is twice as much as of substance $2$. The temperature change for substance $2$ is three times as much as the temperature change for substance $1$.
How does the specific heat of substance $2$ compare to the specific heat of substance $1$?

• A. The specific heat of substance $2$ is $3/2$ as much as the specific heat of substance $1$
• B. The specific heat of substance $2$ is $2/3$ as much as the specific heat of substance $1$
• C. The specific heat of substance $2$ is bigger than the specific heat of substance $1$, but we cannot determined how much bigger
• D. The specific heat of substance $2$ is smaller than the specific heat of substance $1$, but we cannot determined how much smaller
• E. We cannot determine how the specific heat of substance $2$ is related to the specific heat of substance $1$

Answer 1

Answer: (B)

The specific heat of substance $2$ is $2/3$ as much as the specific heat of substance $1$

Given : $m_1=2m_2$ $\Delta T_2=3\Delta T_1$

Let the specific heat of substance $1$ and $2$ be $S_1$ and $S_2$ respectively.

Heat released by one substance must be completely absorbed by another substance i.e $Q_r=Q_a$

$\therefore$ $m_1{S}_1\left(\Delta T_1\right)=m_2{S}_2\left(\Delta T_2\right)$

$\therefore$ $\left(2m_2\right)S_1\left(\Delta T_1\right)=m_2{S}_2\left(3\Delta T_1\right)$ $⟹S_2=\frac{2}{3}{S}_1$

Hence option B is correct.