Two different metal bodies A and B of equal mass are heated at a...

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:

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation

Options

A $\dfrac{8}{3}$
B $\dfrac{3}{8}$
C $\dfrac{3}{4}$
D $\dfrac{4}{3}$

Correct answer

B. $\dfrac{3}{8}$

Step-by-step solution

${\left(\dfrac{\DeltaQ}{\Deltat}\right)}_{A} = {\left(\dfrac{\DeltaQ}{\Deltat}\right)}_{B}$

$m{S}_{A}{\left(\dfrac{\DeltaT}{\Deltat}\right)}_{A} = m{S}_{B}{\left(\dfrac{\DeltaT}{\Deltat}\right)}_{B}$

$\dfrac{{S}_{A}}{{S}_{B}} = \dfrac{{\left(\dfrac{\DeltaT}{\Deltat}\right)}_{A}}{{\left(\dfrac{\DeltaT}{\Deltat}\right)}_{B}} = \dfrac{90 / 6}{120 / 3} = \dfrac{15}{40} = \dfrac{3}{8}$

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