A system S receives heat continously from an electric heaterof power 10 W- The temparature of S become constant at 50-C when the surrounding temparatureis 20-C- After the heater is switched off- S cools from 35-1-C to 34-9-C in 1 minute- The heat capacity of S is

Name: CENGA - Grade 11 - Physics - Thermal properties of matter - Q124
Uploaded: 2022-07-04T10:36:42+05:30
Description: Formula used: nbsp;dQdt=kΔθ, Q=dQdt× t, Q=CΔθ Given: nbsp;dQdt=10 W of electric heater,Δθ=30^∘C, After heater is switched off its takes 1 min from 35.1^ ...

Formula used: nbsp;dQdt=kΔθ, Q=dQdt× t, Q=CΔθ Given: nbsp;dQdt=10 W of electric heater,Δθ=30^∘C, After heater is switched off its takes 1 min from 35.1^ ...

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Standard X

Physics

Household Electrification

A system S re...

Question

A system $S$ receives heat continously from an electric heaterof power $10 W$ . The temparature of $S$ become constant at $50^{\circ} C$ when the surrounding temparatureis $20^{\circ} C$ . After the heater is switched off, $S$ cools from ${35.1}^{\circ} C to {34.9}^{\circ} C in 1$ minute. The heat capacity of $S$ is

100 J /^{\circ} C

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750 J /^{\circ} C

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1500 J /^{\circ} C

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100 J /^{\circ} C

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Solution

The correct option is C $1500 J /^{\circ} C$
Formula used: $\frac{d Q}{d t} = k Δ θ, Q = \frac{d Q}{d t} \times t, Q = C Δ θ$

Given: $\frac{d Q}{d t} = 10 W of electric heater, Δ θ = 30^{\circ} C,$
After heater is switched off its takes $1 min from {35.1}^{\circ} C to {34.9}^{\circ} C$ .

At $50^{\circ} C$ ,
$\frac{d Q}{d t} = k (50 - 20)$
$10 = k (50 - 20)$
$∴ k = \frac{1}{3}$

At an average temperature of $35^{\circ} C$ ,
$\frac{d Q}{d t} = \frac{1}{3} (35 - 20) = 5 J / s$

Heat lost in 1 minute $= \frac{d Q}{d t} \times 60 = 300 J$

Fall in temparature is ${0.2}^{\circ} C = Δ θ$
$∴ C = \frac{Q}{Δ θ} = \frac{300}{0.2} = 1500 J /^{\circ} C$

FINAL ANSWER: (d).

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A system $S$ receives heat continuously from an electrical heater of power $10 W$ . The temperature of $S$ becomes constant at $50^{\circ} C$ when the surrounding temperature is $20^{\circ} C$ . After the heater is switched off, $S$ cools from ${35.1}^{\circ} C$ to ${34.9}^{\circ} C$ in 1 minute. The heat capacity of $S$ is :

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