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(B) Given that the bodies are heated at a uniform rate,the rate of heat supply is constant,i.e.,$\left(\frac{\Delta Q}{\Delta t}\right)_{A} = \left(\f

Vedclass · Accepted Answer

$\frac{3}{8}$

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(B) Given that the bodies are heated at a uniform rate,the rate of heat supply is constant,i.e.,$\left(\frac{\Delta Q}{\Delta t}ight)_{A} = \left(\frac{\Delta Q}{\Delta t}ight)_{B}$.We know that $\Delta Q = mc\Delta T$,so $\frac{\Delta Q}{\Delta t} = mc\left(\frac{\Delta T}{\Delta t}ight)$.Since the masses $m$ are equal,we have $c_{A}\left(\frac{\Delta T}{\Delta t}ight)_{A} = c_{B}\left(\frac{\Delta T}{\Delta t}ight)_{B}$.Therefore,the ratio of specific heat capacities is $\frac{c_{A}}{c_{B}} = \frac{(\Delta T / \Delta t)_{B}}{(\Delta T / \Delta t)_{A}}$.From the graph,the slope $(\Delta T / \Delta t)$ for body $A$ is $\frac{120 - 0}{3 - 0} = 40 \ ^{\circ}	ext{C/s}$.The slope $(\Delta T / \Delta t)$ for body $B$ is $\frac{90 - 0}{6 - 0} = 15 \ ^{\circ}	ext{C/s}$.Thus,$\frac{c_{A}}{c_{B}} = \frac{15}{40} = \frac{3}{8}$.

Two different metal bodies $A$ and $B$ of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is :

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