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. lf the masses of P and Q are the same, calculate the ratio of the specific heat capacities of Q to P.
The heat absorbed by a substance is given by the formula:
Q = m × c × ΔT
For objects P and Q.
- Same quantity of heat (Q) is supplied.
- Same mass (m).
- Temperature change in P is twice that in Q (ΔT\(_P\) = 2 × ΔT\(_Q\)).
For P
Q = m × c\(_P\) × (2 × ΔT\(_Q\))
For Q:
Q = m × c\(_Q\) × ΔT\(_Q\)
Since both equal **Q**, set them equal:
m × c\(_P\) × 2ΔT\(_Q\) = m × c\(_Q\) × ΔT\(_Q\)
Cancel m and ΔT\(_Q\) from both sides:
2 c\(_P\) = c\(_Q\)
Therefore:
\(\frac{c_Q }{ c_P}\) = 2
Ratio c\(_Q : c_P\) = 2 : 1
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