Answer:
Explanation:
Given
Voltage [tex]V=120 V[/tex]
Power [tex]P=450 W[/tex]
mass of water [tex]m=400 gm[/tex]
initial temperature of water [tex]T_i=23^{\circ}C [/tex]
Resistance R is given by
[tex]P=\frac{V^2}{R}[/tex]
[tex]R=\frac{V^2}{P}[/tex]
[tex]R=\frac{120^2}{450}[/tex]
[tex]R=32 \ Omega [/tex]
Heat required to raise water temperature to [tex]100^{\circ}C [/tex]
[tex]Q=mc\Delta T[/tex]
where [tex]c=4.184 kJ/kg-K[/tex] specific heat of water
[tex]Q=0.4\times 4.184\times (100-23)=128.86 kJ[/tex]
time required is
[tex]t=\frac{Q}{P}=\frac{128.86\times 1000}{450}[/tex]
[tex]t=286.37 s\approx 4.77 min[/tex]
