Question

The density of water at $20^{\circ}C$ is $998\, kg/m^3 $ and at $40^{\circ}C$ $992\,kg/m^3 $. The coefficient of volume expansion of water is

• A. $ 3 \times 10^{-4} \,{}^ \circ C$
• B. $ 2 \times 10^{-4} \,{}^ \circ C$
• C. $ 6 \times 10^{-4} \,{}^ \circ C$
• D. $ 10^{-4} \,{}^ \circ C$

Answer 1

Answer: (A)

(a) : As $ P T_s = \frac{ PT_1}{1+ \gamma \Delta T} = \frac{ PT_1}{ 1+ \gamma ( T_2-T_1)}$
Here,$ T_1= 20 ^\circ C, T_2 = 40 ^ \circ C $
$ P_20 = 998 kg / m^3 , P_40 = 992 kg / m^3 $
$ \therefore \, \, \, \, 992 = \frac{998}{ 1+\gamma (40-20)}$
$ 992= \frac{998}{ 1+ 20 \gamma}$
$ 992(1+20\gamma) = 998 $
$1+ 20 \gamma = \frac{998}{992} -1 = \frac{6}{992}$
$\gamma = \frac{6}{992} \times \frac{1}{20}= 3 \times 10^{-4} / ^\circ C$