Question

A liquid P of specific heat capacity 1800 Jkg⁻¹K⁻¹ and at 80°C is mixed with a liquid R of specific heat capacity 1200 Jkg⁻¹K⁻¹ and at 30°C. After mixing, the final temperature of the mixture is 50°C. In what proportion by weight are the liquids mixed?

Answer 1

Substance	Mass	S.H.C.	Initial Temp.	Final Temp. = 50°C
Liquid P	?	1800 Jkg−1K−1	80°C	θF = (80 − 50) = 30°С
Liquid R	?	1200 Jkg−1K−1	30°C	θR = (50 − 30) = 20°С

Heat lost by liquid Р = mcθ_F

= P × 1800 × 30

Heat gained by liquid R = mcθ_R

= R × 1200 × 20

Heat gained = Heat lost

⇒ R × 1200 × 20 = P × 1800 × 30

\[\Rightarrow \frac{P}{R} =\frac{1200 \times 20}{1800 \times 30}\]

\[\Rightarrow \frac{P}{R}=\frac{4}{9}\]

∴ P : R = 4 : 9