Basics of Heat and Temperature Changes

Problem Statement

Consider the relationship between heat and temperature change when water in a cup is heated or cooled. Answer the following questions.

(1) A cup with a heat capacity of $C_0$C0​ contains water. How much heat, in $\mathrm{J}$J, is required to raise the temperature of the entire cup by $\Delta T_0$ΔT0​?

(2) The temperature of a mass $m_1$m1​ of water was raised from $T_a$Ta​ to $T_b$Tb​. What is the amount of heat, in $\mathrm{J}$J, that the water absorbed? Let the specific heat capacity of water be $c_w$cw​.

(3) A constant amount of heat $Q_2$Q2​ was applied to a mass $m_2$m2​ of water in a container using an electric heater, causing the temperature of the water to rise from $T_c$Tc​ to $T_d$Td​. What is the specific heat of this water in $\mathrm{J/(kg\cdot K)}$J/(kg⋅K)? Assume that the heat capacity of the container and heat transfer to the outside can be neglected.

Constraints

・$C_0 = 80 \text{ J/K}$C0​=80 J/K ・$\Delta T_0 = 15 \text{ K}$ΔT0​=15 K ・$m_1 = 0.20 \text{ kg}$m1​=0.20 kg ・$T_a = 280 \text{ K}$Ta​=280 K ・$T_b = 295 \text{ K}$Tb​=295 K ・$c_w = 4200 \text{ J/(kg\cdot K)}$cw​=4200 J/(kg\cdotK) ・$m_2 = 0.50 \text{ kg}$m2​=0.50 kg ・$Q_2 = 31500 \text{ J}$Q2​=31500 J ・$T_c = 285 \text{ K}$Tc​=285 K ・$T_d = 300 \text{ K}$Td​=300 K

Input Format

Let the answer to Part (1) be $A_1\ \mathrm{J}$A1​ J, the answer to Part (2) be $A_2\ \mathrm{J}$A2​ J, and the answer to Part (3) be $A_3\ \mathrm{J/(kg\cdot K)}$A3​ J/(kg⋅K). As your final answer, calculate the value $A_1 + A_2 - A_3$A1​+A2​−A3​ and enter the resulting natural number as is.