The Ultimate Drip Coffee: Energy Path to the Ideal Brewing Temperature

Problem Statement

A skilled barista carefully controls the water temperature for brewing to maximize the flavor of coffee. Using a precise heater, he heats a fixed amount of water and records the relationship between the heat added $Q$Q and the water temperature $T$T on a graph.

The graph shows a straight line (linear function) with the horizontal axis representing the heat added $Q \ [\text{J}]$Q [J] and the vertical axis representing the water temperature $T \ [{}^\circ\text{C}]$T [∘C]. According to the record, the temperature just before heating began ($Q = 0 \ [\text{J}]$Q=0 [J]) was $T_{\text{start}}$Tstart​, and after adding a total heat $Q_{\text{total}}$Qtotal​, the temperature reached the ideal brewing temperature $T_{\text{end}}$Tend​.

Find the total heat $Q_{\text{total}} \ [\text{J}]$Qtotal​ [J] supplied by the heater to the water. Evaporation of water during heating and heat loss to the surroundings can be neglected. The specific heat capacity of water is assumed to be constant regardless of temperature.

Constraints

• Mass of water heated $m$m: $285 \ \text{g}$285 g
• Specific heat capacity of water $c$c: $4.2 \ \text{J}/(\text{g} \cdot \text{K})$4.2 J/(g⋅K)
• Temperature at the start of heating $T_{\text{start}}$Tstart​: $16 \ [{}^\circ\text{C}]$16 [∘C]
• Temperature at the end of heating $T_{\text{end}}$Tend​: $94 \ [{}^\circ\text{C}]$94 [∘C]

Input Format

Give the value of $Q_{\text{total}}$Qtotal​ as a positive integer. Do not include the unit ($\text{J}$J); provide the numerical value only.