Question

Some stoves use the heat produced by current flowing through a conductor. If the heating element (conductor) has a resistance of 30 ohms, how long will the burner have to work to heat 500 g of 30°C water up to its boiling point? The specific heat of water is 4.19 x 103 J/kg·°C, and the household voltage is (120V).

Answer 1

Answer:305.52 s

Step-by-step explanation:

Given

Resistance of conductor
`R=30 \Omega`

mass of water
`m=500 gm`

Initial Temperature
`T_i=30^(\circ)C`

Final Temperature
`T_f=100^(\circ)C`

specific heat
`c=4.19* 10^3 J/kg-^(\circ)C`

Heat required to heat water
`Q=mc\Delta T`

`Q=0.5* 4.19* 10^3* (100-30)`

`Q=146.65* 10^3 J`

Heat generated by stove in time t

`H=(V^2)/(R)* t`

`H=(120^2)/(30)* t`

`(120^2)/(30)* t=146.65* 10^3`

`t=(146.65* 10^3* 30)/(120^2)`

`t=305.52 s\approx 5.09 min`