Question

a bucket of water of volume 15 litre is heated from 20° C to 40°C by an immersion heater of 1500 watt. Time required​

Answer 1

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GiveN :-

• A bucket of water has 15 litres of water .
• The water is heated from 20°C to 40°C by a immersion rod .
• The power of immersion rod is 1500 Watts.

To FinD :-

• The time required .

AnsweR :-

$\underline{\red{\sf \mathscr{A}ccording \ \mathscr{T}o\ \mathscr{Q} uestion :- }}$

$\sf Power \ of \ heater = 1500 Watts \\\\\sf Volume \ of \ bucket \ = \ 15L = 15,000 ml = 15,000 cm^3$

And , we know that the density of water is 1g/cm³ . So ,

$\large\qquad\boxed{\red{\bf \rho_{water}=1g/cm^3}}$

$\tt:\implies Density = \dfrac{mass}{Volume}\\\\\tt:\implies 1g/cm^3 = \dfrac{mass}{15,000 cm^3}\\\\\boxed{\green{\tt\leadsto Mass = 15,000 g = 15kg }}$

$\sf Change \ in \ temperature \ = \Delta T = 40^{\circ}-20^{\circ}=20^{\circ}$

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Now , we know that Power is the rate of doing work . And here work is done in the form of heat energy.

$\qquad\large\orange{\boxed{\purple{\bf P\times t = m \ s \Delta T }}}$

$\tt:\implies Pt = ms \Delta T \\\\\tt:\implies 1500 W \times t = 15000g \times 4.2 \times 20^{\circ} \\\\\tt:\implies t = \dfrac{1500 \times 4.2 \times 20 }{1500} \\\\\underline{\boxed{\blue{\tt \longmapsto Time = 84 s }}}$

$\boxed{\green{\bf \:\pink{\dag}\: Hence\:the\: time\ taken \ is \ 84 \ seconds . }}$

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