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1000 gm water is heated from 27° C to 4 7° C at a constant pressure of 1 bar. The coefficient of volume expansion of water is 0.002/°C and the molar volume of water at 0° C is $18.00 {cm}^{3} / mol$ . The magnitude of work done (in J) by water is :

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answer is 4.

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Detailed Solution

$V_{r^{\circ} C} = V_{0^{-} C} (1 + γ t)$

$γ =$ Coefficient of volume expansion, t = temperature in $^{\circ} C$

$\begin{array}{l} V_{27^{\circ} C} = 1000 (1 + 0.002 \times 27) \\ = 1054 mL \end{array}$

$\begin{array}{l} V_{47^{\circ} C} = 1000 (1 + 0.002 \times 47) \\ = 1094 mL \\ w = - P Δ V \\ = \frac{- 1 \times (1094 - 1054)}{1000} bar litre \\ = \frac{- 4}{100} bar litre = \frac{- 4}{100} \times 100 J \\ = - 4 J \end{array}$

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