Two identical calorimeters A and B contain equal quantities of water at 20°C. A 5 g piece of metal X with specific heat 0.2 cal g⁻¹ °C⁻¹ is dropped into A, and a 5 g piece of metal Y into B. The equilibrium temperatures are 22°C and 23°C, respectively. Both metals were initially at 40°C. If the specific heat of Y is P/85 cal g⁻¹ °C⁻¹, find P.
Physics · Thermodynamics
JEE Advanced

Question

Two identical calorimeters A and B contain equal quantities of water at 20°C. A 5 g piece of metal X with specific heat 0.2 cal g⁻¹ °C⁻¹ is dropped into A, and a 5 g piece of metal Y into B. The equilibrium temperatures are 22°C and 23°C, respectively. Both metals were initially at 40°C. If the specific heat of Y is P/85 cal g⁻¹ °C⁻¹, find P.

Physics · Thermodynamics

G1 Physics · Accepted Answer

Apply energy conservation. Sensible heat is Q=mcΔT and phase-change heat is Q=mL. Heat lost by hotter parts equals heat gained by colder parts. Substituting the given values gives 27.