A piece of metal with a mass of 1.9 kg, speciﬁc heat of 202 J/kg/◦C, and initial temperature of 83◦C is dropped into an insulated jar that contains liquid with a mass of 4 kg, speciﬁc heat of 1000 J/kg/◦C, and initial temperature of 7◦C. The piece of metal is removed after 2.7 s, at which time its temperature is 16◦C. Find the temperature of the liquid after the metal is removed. Neglect any eﬀects of heat transfer to the air or to the insulated jar. Answer in units of ◦C.

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valetta valetta · Answer 1 · 2019-08-09T08:57:09+02:00

Answer:

13.428° C

Explanation:

Given:

Mass of the metal piece, m = 1.9 kg

specific heat of the metal, C = 202 J/kg°C

Initial temperature of the metal, T₁ = 83° C

Final temperature of the metal, T₂ = 16° C

mass of the liquid, M = 4 kg

specific heat of the liquid, C' = 1000 J/kg°C

Initial temperature of the liquid, T₃ = 7° C

Now,

when the metal is removed

The heat lost by the metal = The heat gained by the liquid

thus,

mCΔT = MC'ΔT'

let the final temperature of the liquid be T₄

thus, we have

- [1.9 × 202 × (T₂ - T₁)] = 4 × 1000 × (T₄ - T₃) (here, negative sign depicts the heat lost by the metal)

on substituting the further values, we get

- [1.9 × 202 × (83 - 16)] = 4 × 1000 × (T₄ - 7)

or

T₄ - 7 = 6.42865

or

T₄ = 13.428° C

Hence, the final temperature of the liquid is 13.428° C