Question

A well-insulated copper tank of mass 13 kg contains 4 kg of liquid water. Initially, the temperature of the copper is 27°C and the temperature of the water is 50°C. An electrical resistor of negligible mass transfers 100 kJ of energy to the contents of the tank. The tank and its contents come to equilibrium.

Answer 1

Answer:49.3

Explanation:

Given

mass of water $m_w=4 kg$

mass of tank $m_T=13 kg$

initial of temperature of water =$50^{\circ}C$

initial of temperature of tank=$27^{\circ}C$

Specific heat of water =4.184kJ/kg k

Specific heat of copper=0.386 KJ/kg k

From first law of thermodynamics we have

$Q=\Delta U+W$

Given tank is insulated thus Q=0

$-W=\Delta U$

work will be negative as it is being done on system

$-\left ( -100\right )=\Delta U_{water}+\Delta U_{tank}$

$-\left ( -100\right )=m_w\times c_{water}\left ( T-50\right )+m_Tc_{tank}\left ( T-27\right )$

$100=4\times 4.184\left ( T-50\right )+13\times 0.386\left ( T-27\right )$

$T=49.3^{\circ} C$