Question

$PandQ$ are two blocks of different metals. They have the same volume but block $P$ has twice the mass of block $Q$. When given identical quantities of energy, their temperatures rise by the same amount. Which one of the following statements is true ?

• A. The density of $P$ is half that of $Q$.
• B. The density of $P$ is the same as that of $Q$.
• C. The specific heat capacity of $P$ is half that of $Q$.
• D. The specific heat capacity of $P$ is the same as that of $Q$.

Answer 1

The correct option is C The specific heat capacity of $P$ is half that of $Q$.

Answer is C.
As the mass of P is twice that of Q.
Density = M/V
Density of P (d P) = 2M/V
Density of Q (d Q)= M/V
So, d P/d Q = 2M/M = 2.
d P = 2 d Q, so density of P is twice that of Q which option is not given.
Now, Energy = mass (m) * specific heat capacity (s) * temperature (t).
Energy of P = 2*m*sP*t
Energy of Q = m*sQ*t
Since, the energies are equal, 2*m*sP*t = m*sQ*t
sP / sQ = m / 2m (as t is also same)
That is, sP / sQ = 1 / 2. Therefore, sP = 1/2 sQ.
Hence, the specific heat capacity of P is half that of Q.