Question

Ma puteti ajuta cu rezolvarea acestei probleme de Fizica ?

Un calorimetru cu capacitatea calorica C = 125 J/K contine apa cu masa ma = 0.5kg la temperatura t1 = 20 grade celesius. In calorimetru se introduce o bucata de aluminiu cu masa mAl = 40g, avand temperatura t2 = 80 grade celsius. Ce temperatura finala se stabileste in calorimetru ? (CAl = 920 J/kg * K).

Vreau rezolvarea literar , iar apoi numerica si fara raspunsuri copiate!!!
Multumesc.

Answer 1

[tex]\displaystyle \text{Se da:}\\ \\ C=125\frac JK\\ \\ m_a=0,5kg\\ \\ c_a=4190\frac{J}{kg\times K}\\ \\ t_1=20^\circ C\\ \\ m_{Al}=40g=0,04kg\\ \\ t_2=80^\circ C\\ \\ c_{Al}=920\frac{J}{kg\times K}\\ \\ t=?^\circ C\\ \\ \\[/tex]


[tex]\text{Formule:}\\ \\ \text{Din ecuatia calorimetriei:}\\ \\ \\ Q_{primit}=-Q_{cedat}\\ \\ \\ \text{Aluminiul cedeaza caldura apei SI calorimetrului} \\ \\ \\ Q_0+Q_1=-Q_2\\ \\ \\ \text{Tinind cont ca:}\\ \\ Q=c\times m\times \Delta t=c\times m\times(t_2-t_1)=C\times (t_2-t_1)\\ \\ \\ \text{Si presupunind ca apa nu-si schimba starea de agregare:}\\ \\ \\[/tex]


[tex]C\times(t-t_0)+c_a\times m_a\times(t-t_1)=-c_{Al}\times m_{Al}\times(t-t_2)\\ \\ \\ \text{Deoarece apa se afla deja in calorimetru, }t_0=t_1\\ \\ \\ C\times(t-t_1)+c_a\times m_a\times(t-t_1)=-c_{Al}\times m_{Al}\times(t-t_2)\\ \\ \\ \text{Exprimam t, deschizind parantezele:}\\ \\ \\[/tex]


[tex]C\times t-C\times t_1+c_a\times m_a\times t-c_a\times m_a\times t_1=\\ =-c_{Al}\times m_{Al}\times t+c_{Al}\times m_{Al}\times t_2\\ \\ C\times t+c_a\times m_a\times t+c_{Al}\times m_{Al}\times t=\\ =c_{Al}\times m_{Al}\times t_2+C\times t_1+c_a\times m_a\times t_1\\ \\ t\times(C+c_a\times m_a+c_{Al}\times m_{Al})=\\ =t_1\times (C+c_a\times m_a)+c_{Al}\times m_{Al}\times t_2\\ \\ \\ \boxed{t=\frac{t_1\times (C+c_a\times m_a)+c_{Al}\times m_{Al}\times t_2}{C+c_a\times m_a+c_{Al}\times m_{Al}}}\\ \\ \\[/tex]


[tex]\displaystyle\text{Calcule:}\\ \\ t=\frac{20\times (125+4190\times 0,5)+920\times 0,04\times 80}{125+4190\times 0,5+920\times 0,04}\approx 21^\circ C[/tex]