A solid body at initial temperature T₀ is immersed in a bath of water at initial temperature T_w0. Heat is transferred from the solid to the water at a rate Q̇ = K̇ (T_w – T) , where K is a constant and T_w and T are instantaneous values of the temperatures of the water and solid. Develop an expression for T as a function of time τ. Check your result for the limiting cases, τ = 0 and τ = ∞. Ignore effects of expansion or contraction, and assume constant specific heats for both water and solid.