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

Step-by-step 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* c_(water)\left ( T-50\right )+m_Tc_(tank)\left ( T-27\right )`

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

`T=49.3^(\circ) C`