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Calorimetry

Calculate Δ...

Question

Calculate $Δ U$ and $Δ H$ in calories if 1 mole of a monoatomic ideal gas is heated at constant pressure of 1 atm from $25^{o} C$ to $50^{o} C$ .

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Solution

For monoatomic ideal gas, $C_{v} = \frac{3}{2} R$
$C_{p} = \frac{Δ H}{Δ T}$

$∴ Δ H = C_{p} Δ T m o l^{- 1}$ ( or $n C_{p} Δ T$ for $n$ moles )
$= \frac{5}{2} \times 1.987 \times 25 = 124.2 c a l$
Work done,
$w = - P Δ V = - P (V_{2} - V_{1})$
$= - (P V_{2} - P V_{1}) = - (n R T_{2} - n R T_{1})$
$= - m R (T_{2} - T_{1})$
$= - 1 \times 1.987 (323 - 298) c a l$
$= - 49.7 c a l$
$Δ E = q + w$
$= 124.2 - 49.7 c a l = 74.5 c a l$ .

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