A solid of mass m has temperature-dependent specific heat as C(T) = C_0 + α T , where C_0 and α are constants. The solid is heated from T_1 to T_2 . Which one of the following is the correct expression for quantity of

Question

Quantrex Academy · Accepted Answer

Correct answer: D. Q = m(T_2 - T_1) [C_0 + (α)/(2)(T_1 + T_2)]

The quantity of heat dQ required to raise the temperature of a mass m by dT is given by: dQ = m C(T) dT Substituting the given specific heat C(T) = C_0 + α T : dQ = m (C_0 + α T) dT Integrating both sides from T_1 to T_2 : Q = ∫_ T_1 ^ T_2 m (C_0 + α T) dT Q = m [ C_0 T + (α T^2)/(2) ]_ T_1 ^ T_2 Q = m [C_0 (T_2 - T_1) + (α)/(2) (T_2^2 - T_1^2) ] Using the identity T_2^2 - T_1^2 = (T_2 - T_1)(T_2 + T_1) : Q = m (T_2 - T_1) [C_0 + (α)/(2) (T_1 + T_2) ] Answer: Q = m(T_2 - T_1) [C_0 + (α)/(2)(T_1 + T_2)]

A solid of mass m has temperature-dependent specific heat as C(T) =...

Options

Correct answer

Step-by-step solution

More from General Science