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.
Δθ\(_P\) = 2 × Δθ\(_Q\)
m\(_P\) = m\(_Q\)
c\(_Q\) = c\(_P\) = ?
H\(_P\) = H\(_Q\) (given)
i.e. m\(_P\) × c\(_P\) × Δθ\(_P\) = m\(_Q\) × c\(_Q\) × Δθ\(_Q\)
Since Δθ\(_P\) = 2 × Δθ\(_Q\) and m\(_P\) = m\(_Q\)
∴ m\(_Q\) × c\(_P\) × 2 × Δθ\(_Q\) = m\(_Q\) × c\(_Q\) × Δθ\(_Q\)
c\(_P\) × 2 = c\(_Q\)
\(\frac{c_Q}{c_P}\) = \(\frac{2}{1}\)
\(\therefore\) c\(_Q\): c\(_P\) = 2: 1
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