1. Tardigrade
  2. Question
  3. Chemistry
  4. The coefficient of thermal expansion, α, is nearly constant for a liquid α=(1/V)((dV/dT))P At 293 K and 1 atm for water α = 2.1 K-1 What is the approximate work done when 1 mole of liquid is heated from 288 K to 298 K at 1 atm ? Molar volume of liquid = 18 ml?

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Q. The coefficient of thermal expansion, $\alpha$, is nearly constant for a liquid $\alpha=\frac{1}{V}\left(\frac{dV}{dT}\right)_{P}$
At $293 K$ and $1 atm$ for water $\alpha = 2.1 K^{-1}$ What is the approximate work done when $1$ mole of liquid is heated from $288 K$ to $298 K$ at $1 atm$ ? Molar volume of liquid $= 18 ml?$

Thermodynamics

Solution:

$dV=\alpha VdT$
$\Delta W=-\int PdV=-\alpha V\times P \int_{T_1}^{T_{2}} dT$
or $\Delta W=-2.1\times18\times10^{-6}\times10^{5}\times10 J$
or $\Delta W=-2.1\times18\, J$
or $\Delta W=-37.8\, J$