Question

Explain briefly, how you would determine the specific heat capacity of a liquid?

Answer 1

In this case, take any solid of known specific heat and a liquid, whose specific heat capacity is to be determined. The solid chosen should be insoluble and non reactive with the liquid. The observations are to be noted as below:

(i) Mass of empty calorimeter with strirrer = m₁ gm.

(ii) Mass of calorimeter + Liquid (or unknown sp. heat) = m₂ gm.

(iii) Mass of solid = M gm.

(iv) Specific heat of solid (J/ gm/ °C) = 'S₁' 

(v) Initial temp. of liquid (as well as calorimeter) = t₁ °C

(vi) Temperature of hot solid = t₂ °C 

(vii) Final temperature of the mixture = t°C.

Calculation: Let 's' be the specific heat capacity of the liquid.

(i) Fall in temperature of the hot solid = (t₂ - t₁)°C

(ii) Rise in temperature of the liquid = (t - t₁)°C

(iii) Rise in temperature of calorimeter = (t - t₁)°C

(iv) Heat given out by hot solid = M × s₁ × (t₂ - t)

(v) Heat taken up by liquid = (m₂ - m₁) × s × (t - t₁)

(vi) Heat taken up by calorimeter = m₁ × 0.4 × (t - t₁) 

Hence, heat taken up by liquid + Heat taken up by calorimeter = Heat given out by solid

or (m₂ - m₁) × s × (t - t₁) + m₁ × 0.4 × (t - t₁) = M × s₁ × (t₂ - t) 

From this heat equation, we get 

s = `("M" xx "s"_1 xx ("t"_2 - "t") - "m"_1 xx 0.4 ("t" - "t"_1))/(("m"_2 - "m"_1)("t" - "t"_1))` J/gm/°C