Two identical calorimeters contain equal water quantities initially at 20°C. A 5 g sample of metal X (specific heat 0.2 cal g⁻¹ °C⁻¹) at 40°C makes calorimeter A reach 22°C. A 5 g sample of metal Y at 40°C makes calorimeter B reach 23°C. If the specific heat of Y is 9K/85 cal g⁻¹ °C⁻¹, find K.
Physics · Mixed Chapter
JEE Mains

Question

Two identical calorimeters contain equal water quantities initially at 20°C. A 5 g sample of metal X (specific heat 0.2 cal g⁻¹ °C⁻¹) at 40°C makes calorimeter A reach 22°C. A 5 g sample of metal Y at 40°C makes calorimeter B reach 23°C. If the specific heat of Y is 9K/85 cal g⁻¹ °C⁻¹, find K.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Effective water-plus-calorimeter heat capacity: Let C be the common heat capacity (cal/°C). For metal X, 5×0.2×(40−22) = C(22−20), so 18=2C ⇒ C=9 cal/°C. Step 2 — Energy balance for metal Y: 5c₂(40−23) = C(23−20) ⇒ 85c₂ = 27. Step 3 — Specific heat of Y: c₂=27/85 cal g⁻¹ °C⁻¹. Step 4 — Compare with 9K/85: 9K=27 ⇒ K=3. Answer: 3.