JAMB Physics 2017 Paper

Concept:Use the heat formula $H = mc\Delta\theta$ to compare the two objects.Explanation:Let the mass of Q be $m$ and its temperature change be $\theta$.Then the mass of P is $\frac{1}{2}m$ and the temperature change of P is $2\theta$.Since both objects are supplied with the same quantity of heat, $H_P = H_Q$.Using $H = mc\Delta\theta$:$H_P = \left(\frac{1}{2}m\right)c_P(2\theta) = m c_P \theta$$H_Q = m c_Q \theta$Equating the two gives $m c_P \theta = m c_Q \theta$.Cancelling $m$ and $\theta$, we get $c_P = c_Q$.Therefore, the ratio is $\frac{c_P}{c_Q} = \frac{1}{1}$.Answer:The ratio of the specific heat capacity of P to Q is $1:1$, i.e. option C.