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');--grs:50px;--gtaos:105px;--gtaosi:-105px;--gtaof:210px;--gbes:calc(100% + 105px);--gbef:calc(100% + 210px);--gbet:translateX(-105px);--gbeti:translateX(105px);--vgc:repeat(12, 1fr);--gc1:repeat(12, 1fr);--gc2:repeat(6, 1fr);--gc3:repeat(4, 1fr);--gc3h:1/4;--gc4:repeat(3, 1fr);--gcm:8.333%;--gac:1fr;--gcw50:50%;--gc2tp:0 calc(var(--grs) * 2) 0 0;--gc2sw:var(--gbes);--gc2slpl:0 0 0 105px;--gc2srpf:0 105px 0 0;--gc2sof:1;--gc2sol:2;--gc50:4/span 6;--gc48a:1/5;--gc48b:5/-1;--gc84a:1/9;--gc84b:9/-1;--gc39a:1/4;--gc39b:4/-1;--gc93a:1/10;--gc93b:10/-1;--gc615a:1/7;--gc615b:8/-1;--gc516a:1/6;--gc516b:7/-1;--tppr:0;--bgp:42px;--s_cn:0;--s_ces:4px;--s_cest:4px 4px 0 0;--s_cesb:0 0 4px 4px;--s_cs:8px;--s_cm:12px;--s_cl:16px;--s_cls:16px 0 0 16px;--s_cle:0 16px 16px 0;--s_clt:16px 16px 0 0;--s_cel:28px;--s_celt:28px 28px 0 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Consideriamo la riduzione della pressione di vapore. Possiamo calcolare la variazione di energia che accompagna una variazione di pressione utilizzando la prima legge della termodinamica. Se lasciamo che il simbolo U rappresenti l'energia in un sistema e calcoliamo la variazione di U che si verifica quando cambiamo il volume, a pressione costante (supponiamo che non venga aggiunto o rimosso calore) possiamo scrivere
dU rappresenta una piccola variazione di energia e dV rappresenta una piccola variazione di volume. La relazione tra pressione e volume, detta legge dei gas ideali, è la seguente
dove n è il numero di moli di gas, R è una costante, nota come costante dei gas (8,31 J/mol K) e T è la temperatura del gas in kelvin. Possiamo differenziare la legge dei gas ideali per ottenere dV
Combinando questo con la prima legge si ottiene
Ora, l'energia necessaria per passare dalla pressione di vapore dell'acqua pura nel bicchiere, che chiamiamo pressione di vapore di saturazione o p0, alla pressione di vapore dell'acqua nella spugna è
Il rapporto p /p0 è chiamato attività dell'acqua (aw) quando si parla di acqua nella spugna o di acqua negli alimenti o in altri solidi o liquidi. Lo chiamiamo umidità relativa quando lo applichiamo all'acqua nell'aria e talvolta lo moltiplichiamo per 100 per esprimerlo in percentuale. Il rapporto U/n è l'energia per mole di acqua ed è chiamato potenziale idrico, con il simbolo Ψ. Il potenziale idrico ha come unità di misura i Joule/mole. Con questa sostituzione, si arriva infine all'equazione che mette in relazione l'energia dell'acqua nella spugna e la sua attività idrica
L'equazione significa che possiamo esprimere lo stato energetico dell'acqua in un prodotto come potenziale idrico o come attività idrica. Alcuni campi della scienza utilizzano il potenziale idrico e altri l'attività dell'acqua. Alcuni usano anche la depressione del punto di congelamento o l'osmolalità, ma sono tutti concetti equivalenti. Ciascuno di essi presenta vantaggi e svantaggi, ma la cosa importante da capire è che tutti sono misure dello stato energetico dell'acqua e hanno una solida base teorica. L'attività dell'acqua è la misura più utilizzata nella scienza e nell'ingegneria alimentare con precisi misuratori di attività dell'acqua.
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