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 in Q. If the masses of P and Q are the same, calculate the ratio of the specific heat capacities of Q to P.
A
4: 1
B
2: 1
C
1: 2
D
1: 1
Verified Correct Answer: B.
Physical Principles & Numerical Solution
\Delta\theta\(_P\) = 2 \times \Delta\theta\(_Q\)
m\(_P\) = m\(_Q\)
c\(_Q\) = c\(_P\) = ?
H\(_P\) = H\(_Q\) (given)
i.e. m\(_P\) \times c\(_P\) \times \Delta\theta\(_P\) = m\(_Q\) \times c\(_Q\) \times \Delta\theta\(_Q\)
Since \Delta\theta\(_P\) = 2 \times \Delta\theta\(_Q\) and m\(_P\) = m\(_Q\)
∴ m\(_Q\) \times c\(_P\) \times 2 \times \Delta\theta\(_Q\) = m\(_Q\) \times c\(_Q\) \times \Delta\theta\(_Q\)
c\(_P\) \times 2 = c\(_Q\)
\(\frac{c_Q}{c_P}\) = \(\frac{2}{1}\)
\(\therefore\) c\(_Q\): c\(_P\) = 2: 1
Source: WAEC / JAMB / NECO Classroom Archive (Record #76363)