Question

Initially k₁ is closed, now if k₂ is also closed. Find the heat loss –

• A. $\frac{1}{2}$CV²
• B. $\frac{2}{3}$CV²
• C. $\frac{1}{3}$CV²
• D. $\frac{1}{4}$CV²

Answer 1

Answer: (C)

$\frac{1}{3}$CV²

Answer 2

When k₁ is closed

Q = CV

energy U_i =$\frac { 1 } { 2 }$ CV²

When k₂ is also closed

equivalent ckt

C_eq = C + =

Energy U_f =$\frac { 1 } { 2 }$× V² = $\frac { 5 } { 6 }$CV²

charge supplied by battery after closing k₂

= $\frac { 5 } { 3 }$CV – CV = $\frac { 2 } { 3 }$CV

energy supplied by battery = U_f – U_i + DH

$\frac { 2 } { 3 }$CV² = $\frac { 5 } { 6 }$CV² –$\frac { 1 } { 2 }$CV² + DH

\ DH = $\frac { 1 } { 3 }$ CV²