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.
A
4 : 1
B
2 : 1
C
1 : 1
D
1 : 2
E
1 : 4.
Verified Correct Answer: B.
Physical Principles & Numerical Solution
The heat absorbed by a substance is given by the formula:
Q = m \times c \times \DeltaT
For objects P and Q.
- Same quantity of heat (Q) is supplied.
- Same mass (m).
- Temperature change in P is twice that in Q (\DeltaT\(_P\) = 2 \times \DeltaT\(_Q\)).
For P
Q = m \times c\(_P\) \times (2 \times \DeltaT\(_Q\))
For Q:
Q = m \times c\(_Q\) \times \DeltaT\(_Q\)
Since both equal **Q**, set them equal:
m \times c\(_P\) \times 2\DeltaT\(_Q\) = m \times c\(_Q\) \times \DeltaT\(_Q\)
Cancel m and \DeltaT\(_Q\) from both sides:
2 c\(_P\) = c\(_Q\)
Therefore:
\(\frac{c_Q }{ c_P}\) = 2
Ratio c\(_Q : c_P\) = 2 : 1
Source: Myschool Past Questions Archive (Record #25072)