A solid of mass m has temperature-dependent specific heat as C(T) = C₀ + T , where C₀ and are constants. The solid is heated from T₁ to T₂ . Which one of the following is the correct expression for quantity of heat (Q) of the solid mass?

Step-by-step solution

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) = C₀ + T : dQ = m (C₀ + T) dT Integrating both sides from T₁ to T₂ : Q = _ T₁ ^ T₂ m (C₀ + T) dT Q = m [ C₀ T + T^2 2 ]_ T₁ ^ T₂ Q = m [ C₀ (T₂ - T₁) + 2 (T₂^2 - T₁^2) ] Using the identity T₂^2 - T₁^2 = (T₂ - T₁)(T₂ + T₁) : Q = m (T₂ - T₁) [ C₀ + 2 (T₁ + T₂) ] Answer: Q = m(T₂ - T₁) [C₀ + 2 (T₁ + T₂) ]