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Q.

The external pressure 2 atm is applied on frictionless movable piston, fitted in a vessel containing 100 g of X(l) at 450 K. Now heat is supplied keeping pressure constant till 40 g of 500 K is evaporated to from X (g) at 500 K (boiling point). Calculate change in internal $(Δ U)$ energy in kJ for overall process. Assume vapour of X(l) behaves like an ideal gas.
Given : Molar heat capacity of X(l) = 60 J/mole K·
$Δ H_{vaporisation} = 30 kJ / mol; R = 8.3 J / mol - K$
At weight of X = 20 g/mol.

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answer is 6670.

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Detailed Solution

Change in internal energy is the sum of work done and heat transferred. Thus,

$\begin{array}{l} Δ U = Q + w \\ = n_{C_{P_{m}}} Δ T + n Δ H_{vap} + w \\ = \frac{100}{20} \times \frac{60}{1000} \times 50 + \frac{40}{20} \times 30 - Δ n_{g} R T \\ = 15 + 60 - \frac{2 \times 8.3 \times 500}{1000} \\ = 66.7 kJ \Rightarrow 6670 J \end{array}$

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The external pressure 2 atm is applied on frictionless movable piston, fitted in a vessel containing 100 g of X(l) at 450 K. Now heat is supplied keeping pressure constant till 40 g of 500 K is evaporated to from X (g) at 500 K (boiling point). Calculate change in internal (ΔU) energy in kJ for overall process. Assume vapour of X(l) behaves like an ideal gas.Given : Molar heat capacity of X(l) = 60 J/mole K·ΔHvaporisation =30kJ/mol;R=8.3J/mol−KAt weight of X = 20 g/mol.