Question

Three bodies A, B and C of masses m, m and $\sqrt{3}\text{m}$ respectively are supplied heat at a constant rate. The change in temperature $\theta$ versus time t graph for A, B and C are shown by I, II and III respectively. If their specific heat capacities are $S_A,S_B$ and $S_C$ respectively then which of the following relation is correct? (Initial temperature of body is $0^{\circ }C$)

• A. $S_A>S_B>S_C$
• B. $S_B=S_C<S_A$
• C. $S_A=S_B=S_C$
• D. $S_B=S_C>S_A$

Answer 1

The correct option is D

$S_B=S_C>S_A$

If R is rate of heating

$\Delta Q=\text{ms}\left(\theta \right)$

$Rt=\text{ms}\left(\theta \right)\Rightarrow \theta =\left(\frac{R}{\text{ms}}\right)t$

Slope of $\theta -\text{t}$ curve $=\frac{R}{\text{ms}}=\text{tan}\varphi$

$\therefore \text{s}=\frac{R}{\text{m}\times \text{slope of}\theta -\text{t curve}}$

$\Rightarrow S_A=\frac{R}{m\sqrt{3}},S_B=\frac{R}{m},S_C=\frac{R}{\sqrt{3}m.\frac{1}{\sqrt{3}}}=\frac{R}{m}$

$\therefore S_B=S_C>S_A$