A liquid P of specific heat capacity $1800 J k g^{- 1} K^{- 1}$ and at $80^{o} C$ is mixed with a liquid R of specific heat capacity $1200 J k g^{- 1} K^{- 1}$ and at $30^{o} C$ . After mixing, the final temperature of mixture is $50^{o} C$ . In what proportion by weight are the liquids mixed?

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Solution

For Liquid P:
$M a s s = ?$
$S . H . C = 1800 J k g^{- 1} K^{- 1}$
$I n i t i a l T e m p . = 80^{o} C$
$F i n a l T e m p . = 50^{o} C$
$= θ_{F} = (80 - 50) = 30^{o} C$
for Liquid R:
$M a s s = ?$
$S . H . C = 1200 J k g^{- 1} K^{- 1}$
$I n i t i a l T e m p . = 30^{o} C$
$F i n a l T e m p . = 50^{o} C = θ_{F} = (50 - 30)$
$= 20^{o} C$
$H e a t l o s t b y l i q u i d P = m c θ_{F} = P \times 1800 \times 30$
$H e a t g a i n e d b y l i q u i d R = m c θ_{R} = R \times 1200 \times 20$
$H e a t g a i n e d = H e a t l o s t$
$R \times 1200 \times 20 = P \times 1800 \times 30$

$\frac{P}{R} = \frac{1200 \times 20}{1800 \times 30} = \frac{4}{9}$
$P : R = 4 : 9$

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