Question

Two substances $A$ and $B$ have specific heats $c$ and $2c$ respectively. If $A$ and $B$ are given $Q$ and $4Q$ amounts of heat respectively, the change in their temperatures is same. If the mass of $A$ is $m$, what is the mass of $B$?

• A. $m$
• B. $2m$
• C. $3m$
• D. $4m$

Answer 1

The correct option is B $2m$

As we know, $Q=mc\Delta T$
where, $Q$ is the amount of heat given or absorbed by the substance, $m$ is the mass of the substance and $\Delta T$ is the change in temperature.

For Substance A,
$Q_A=m_A{c}_A\Delta T_A$
and for Substance B,
$Q_B=m_B{c}_B\Delta T_B$
Given, mass of substance A, $m_A=m$, $Q_A=Q$, $Q_B=4Q$, $c_A=c$ and $c_B=2c$
According to question,
$\Delta T_A=\Delta T_B$
or, $\frac{Q_A}{m_A{c}_A}=\frac{Q_B}{m_B{c}_B}$
$\frac{Q}{m\times c}=\frac{4Q}{m_B\times 2c}$
$\Rightarrow m_B=2m$