Q136 / 160 · TS EAMCET 2023 (14 May Shift 1) · Physics

If the ratio of densities of two substances is $5: 6$ and the ratio of their specific heat capacities is $3: 5$, then the ratio of heat energies required per unit volume so that the two substances can have same temperature rise is

  • A
    1:1
  • B
    1:4
  • Correct answer
    C
    1:2
  • D
    1:3

Solution

Ratio of densities of two substance, $\frac{\mathrm{d}_1}{\mathrm{~d}_2}=\frac{5}{6}$ Ratio of their specific heat capacities, $\frac{c_1}{c_2}=\frac{3}{5}$ $$ \begin{aligned} & \Delta Q=m c \Delta T=d c \Delta T \\ & \Delta Q_1=d_1 c_1 \Delta T \\ & \Delta Q_2=d_2 c_2 \Delta T \\ & \frac{\Delta Q_1}{\Delta Q_2}=\frac{d_1 c_1}{d_2 c_2}=\frac{5}{6} \times \frac{3}{5}=\frac{1}{2} \end{aligned} $$

Hence, the correct answer is option: 'C'.

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