Question

A solid of mass 80 g and at 75°C is dropped into 150 g of water at 15°C, which is contained in a copper calorimeter of mass 50 g. The final temperature attained by the mixture is 25°C. If the specific heat capacity of copper and water is 400 Jkg⁻¹K⁻¹ and 4200 Jkg⁻¹K⁻¹ respectively, calculate the sp. heat capacity of the solid in SI system.

Answer 1

Substance	Mass	S.H.C.	Initial Temp.	Final Temp. = 25°C
Solid	80 g	?	75°C	θF = (75 − 25) = 50°C
Water	150 g	4.2 Jg−1°C−1	15°C	θR = (25 − 15) = 10°C
Calorimeter	50 g	0.40 Jg−1°C−1	15°C

Heat lost by the solid = mcθ_F

= 80 × c × 50

= 4000 с

Heat gained by water = mcθ_R

= 150 × 4.2 × 10

= 6300 J

Heat gained by the calorimeter = mcθ_R

= 50 × 0.40 × 10

= 200 J

Total heat gained = 6300 J + 200 J = 6500 J

Heat lost = Heat gained

4000 × c = 6500

\[c =\frac{6500}{4000}\]

= 1.625 Jg⁻¹°C⁻¹

= 1625.0 Jkg⁻¹K⁻¹