Question

Equal volumes of copper and mercury have the same themal capacity. Mercury has a specific heat of $0.046$ and density $13.6g$ $c{c}^{-1}$. Calculate the density of copper if its specific heat is $0.092$.

Answer 1

Given: Equal volumes of copper and mercury have the same thermal capacity. Mercury has a specific heat of 0.046 and density $13.6gc{c}^{-1}$.

To find the density of copper if its specific heat is 0.092.

Solution:

Specific heat of mercury, $s_m=0.046$

Density of mercury, ${\rho }_m=13.6c{c}^{-1}$

Specific heat of copper, $s_c=0.092$

As per the given criteria,

Copper and mercury have equal volumes.

$V_c=V_m$

Also given, copper and mercury have same thermal capacity, so

$m_c{s}_c\left(\Delta T\right)=m_m{s}_m\left(\Delta T\right)$

where $m_c,m_m$ are the mass of copper and mercury respectively

and $s_c,s_m$ are the specific heat of copper and mercury respectively

We know, $\text{Density}=\frac{\text{mass}}{\text{volume}}$

$⟹{\rho }_c\times V_c\times s_c\times \left(\Delta T\right)={\rho }_m\times V\times s_m\times \left(\Delta T\right)⟹{\rho }_c\times s_c={\rho }_m\times s_m⟹{\rho }_c=\frac{{\rho }_m\times s_m}{s_c}⟹{\rho }_c=\frac{13.6\times 0.046}{0.092}⟹{\rho }_c=6.8c{c}^{-1}$

is the density of copper if its specific heat is 0.092.