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 :

Solution

Physics sir · 3 steps

Same mass, same heating rate: the steeper line belongs to the smaller specific heat.

1. Heat balance. Both bodies get heat at the same rate P. In time Δ t the heat supplied is P Δ t = m s Δ T. For equal m and P, s is inversely proportional to the slope (Δ T)/(Δ t) of the rising part of the graph.

   s = P/m·1/(Δ T/Δ t) ⇒ s_A/s_B = (Δ T/Δ t)_B/(Δ T/Δ t)_A

2. Read the slopes. A rises from 0 to 120 °C in 3 s, a slope of 40 °C s⁻¹. B rises from 0 to 90 °C in 6 s, a slope of 15 °C s⁻¹. The flat parts are melting and do not affect specific heat.
3. So. s_A/s_B = 15/40 = 3/8, which is option (b).

The idea to keep. On a temperature-time graph with equal mass and equal heating rate, specific heat goes as 1 over the slope. A steeper line means a smaller specific heat.

Answer from the NTA final answer key. Solution by PrepWiser.