Esercizi di "Fenomeni di Trasporto"

Conversioni tra grandezze di concentrazione

Es. cA, xA, fA e wA

Es. (i) cA -> xA (ii) xA -> xA^V (iii) cA -> xA^V (iv) fA -> wA (v) wA -> wA^V (vi) cA -> jA

(i) xA = mA/mT = mA/(VT/(vT/VT)) = cA/cT = cA . v_m,T

(ii) xA = mA/mT . (mT - mA)/(mT - mA) = xA . (mT - mA)/mT = xA (1 - xA) => xA/(1 - xA) = xA

xA = mA/(mT - mA) = (mA/mT) . mT/(mT - mA) = xA . 1/(1 - xA) OK

= xA . (mA + (mT - mA))/(mT - mA) = xA . (xA + 1) => xA = xA/(1 + xA)

(iii) xA = mA/(mT - mA) = xA/(1 - xA) = cA . v_m,T/(1 - cA . v_m,T) = cA . 1/(cT - cA)

(iv) wA = mA/mT = fA . VT/mT = fA/fT

(v) wA' = mA/mT = (mT - mnonA)/mT = 1 - mnonA/mT = 1 - 1/(wA + 1) = wA/(wA + 1)

(vi) jA = mA/VT = (mA/VT) . (P.M.)A = (P.M.)A cA

Es. wA, cA e xA

Es. (i) wA -> cA^v (ii) cA -> cA^v (iii) xA -> wA (iv) wA -> xA^v (v) xA -> xA^v

(i) cA^v = VA/VT = mA/mT . PT/PA = wA . PT/PA

(ii) cA^v = VA/VT = mA/VT = cA . v_m,A

(iii) wA = mA/mT = (mA/VT) . (VT/mT) = xA . (P.M.)A/(P.M.)T

(iv) xA^v = VA/VT = mA/mT . vA/mA = wA . PT/PA

(v) xA^v = VA/VT = mA/VT = xA . v_m,A/v_m,T

Es. cA verso wA e xA

Es. (i) cA -> wA (ii) cA -> xA^V (iii) cA -> wA^V (iv) cA -> xA^V

(i) wA = mA/mT = mA . (P.M.)A/(VT . pT) = cA (P.M.)A/pT = cA . v_m,T . (P.M.)A/(P.M.)T

(ii) xA^V = VA/VT = mA/VT . (VA/mA) = cA . v_m,A = cA^v

(iii) wA = mA/(mT - mA) = (mT - mnonA)/mnonA = mT/(mT - mA) - 1 = 1/(1 - wA) - 1 = wA/(1 - wA)

= (mA/mT)/(1 - (mA/mT)) = mA/VT . (P.M.)A/pT = cA . (P.M.)A/pT . 1/(1 - (P.M.)A/pT) = cA . (P.M.)A/(pT - (P.M.)A cA)

(iv) xA^V = VA/(VT - VA) = VT/VT - VA = 1/(1 - xA) - 1 = (1 - 1 + xA)/(1 - xA) = xA/(1 - xA) = v_m,A cA/(1 - v_m,A cA)

Es. pA verso xA e wA

Es. (i) pA -> xA (ii) pA -> xA^V (iii) pA -> xA (iv) pA -> wA (v) pA -> xA^V

(i) xA = mA/mT = mA/mT . 1/(P.M.)A = xA . (P.M.)T/(P.M.)A => wA = xA . (P.M.)A/(P.M.)T

xA = 1/(P.M.)A . mA/mT = 1/(P.M.)A . v_m,T mA/VT = pA . v_m,T/(P.M.)A

(ii) xA^v = VA/VT = mA/VT . 1/pA = pA . 1/pA

(iii) xA = mA/(mT - mnonA) = mT/(mT - mA) = 1/(mT - mA) = 1/(1 - xA) - 1 = (1 - 1 + xA)/(1 - xA)

= xA/(1 - xA) = ((v_m,T)/(P.M.)A) . pA = pA . v_m,T/(P.M.)A - v_m,T pA

Es. c_A, x_A, s_A e w_A

Es. (i) c_A -> x_A (ii) x_A -> x^v_A (iii) c_A -> X_A (iv) s_A -> w_A (v) W_A -> w_A (vi) c_A -> p_A

(i) x_A = m_A/m_T = m_A/(v_T/(v_T)) = c_A/c_T = c_A . v_m,T

(ii) x_A = m_A/m_T . (m_T - m_A)/(m_T - m_A) = X_A . (m_T - m_A)/m_T = X_A (1 - x_A) => x_A/(1 - x_A) = X_A

X_A = m_A/(m_T - m_A) = x_A/(1 - x_A) = c_A . v_m,T/(1 - c_A . v_m,T) = c_A . 1/(c_T - c_A)

(iv) W_A = m_A/m_T = s_A . v_T/m_T = s_A/s_T

(v) w_A = m_A/m_T = (m_T - m_nonA)/m_T = 1 - m_nonA/m_T = 1 - 1/(w_A + 1) = w_A/(w_A + 1)

(vi) s_A = m_A/v_T = (m_A/v_T) . (P.M.)_A = (P.M.)_A c_A

Es. w_A, c_A e x_A

Es. (i) w_A -> c^v_A (ii) c_A -> c^v_A (iii) x_A -> w_A (iv) w_A -> x^v_A (v) x_A -> x^v_A

(i) c^v_A = V_A/V_T = m_A/m_T . p_T/p_A = w_A p_T/p_A

(ii) c^v_A = V_A/V_T = m_A/V_T . v_m,A = c_A v_m,A

(iii) w_A = m_A/m_T = (m_A/m_T) . (m_A/m_A) = x_A . (P.M.)_A/(P.M.)_T

(iv) x^v_A = V_A/V_T = m_A/m_T . V_A/V_T = w_A . p_T/p_A

(v) x^v_A = V_A/V_T = m_A/m_T . v_m,A/v_m,T = x_A . v_m,A/v_m,T

Es. c_A verso w_A, x^v_A e W_A

Es. (i) c_A -> w_A (ii) c_A -> x^v_A (iii) c_A -> W_A (iv) c_A -> x^v_A (v) p_A -> x_A

(i) w_A = m_A/m_T = m_A . (P.M.)_A/(V_T . p_T) = c_A (P.M.)_A/p_T

(ii) x^v_A = V_A/V_T = m_A/V_T . (V_A/m_A) = c_A v_m,A = c_A^v