Physics 2022 JAMB Past Questions - Question 6: When two objects P and Q are supplied with the same quantity of heat, the temperature change in p is observed to be twice that of Q. The mass of P is half that of Q. The ratio of the specific heat of P to Q is

Correct Answer

D

Explanation

To find the ratio of the specific heat of P to Q, we can use the formula:

\( \frac{m_p}{m_q} = \frac{c_q}{c_p} \)

Where:
\( m_p \) = mass of object P
\( m_q \) = mass of object Q
\( c_p \) = specific heat of object P
\( c_q \) = specific heat of object Q

Given that the temperature change in P is observed to be twice that of Q and the mass of P is half that of Q, we can use the following relationships:

\( \frac{\Delta T_p}{\Delta T_q} = 2 \)
\( m_p = \frac{1}{2} m_q \)

We know that the heat supplied is the same for both objects, so we can use the formula:

\( Q = mc\Delta T \)

Where:
\( Q \) = heat supplied
\( m \) = mass
\( c \) = specific heat
\( \Delta T \) = temperature change

Since the heat supplied is the same for both objects, we can write:

\( m_p c_p \Delta T_p = m_q c_q \Delta T_q \)

Substituting the given relationships, we get:

\( \frac{1}{2} m_q c_p \cdot 2 = m_q c_q \)
\( m_q c_p = 2m_q c_q \)
\( \frac{c_p}{c_q} = 2 \)

So, the ratio of the specific heat of P to Q is 2:1.