Question

If I place a solid hot metal in a cool liquid, the metal and the liquid come to some final temperature together. The specific heat of the liquid is five times as great as the specific heat of the metal. The temperature change for the metal is twenty time as much as that for the liquid.
How does the mass of the liquid compare to the mass of the solid metal? Assume no heat is lost from the system.

• A. The mass of the liquid is $100$ times as much as of the metal
• B. The mass of the liquid is $5$ times as much as the mass of the metal
• C. The mass of the liquid is $20$ times as much as the mass of the metal
• D. The mass of the liquid is $1/4$ as much as the mass of the metal
• E. The mass of the liquid is $4$ times as much as the mass of the metal

Answer 1

The correct option is E The mass of the liquid is $4$ times as much as the mass of the metal

Equal amount of heat must flow from hotter body to colder body to attain thermal equilibrium using conservation of energy.

Thus $m_{solid}{s}_{solid}\Delta T_{solid}=m_{liquid}{s}_{liquid}\Delta T_{liquid}$

$⟹\frac{m_{liquid}}{m_{solid}}=\frac{1}{5}\times \frac{20}{1}=4$