A system is supplied power of 10 W- The temperature of the system becomes constant at 50-C- with temperature of surrounding at 20-C- When power is switched off system cools from t-C to t-n-C in one minute- The heat capacity of the system is 1200 J-C- Find the limiting value of n-

We know that dQdt= K(T T_0) Power, P=10 W, nbsp; Temperature of the system =50^∘C, nbsp; Temperature of surrounding =20^∘C, nbsp; Heat capacity of the ...

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Standard VI

Physics

Electric Bulb and Its Working

A system is s...

Question

A system is supplied power of $10 W$ . The temperature of the system becomes constant at $50^{\circ} C$ , with temperature of surrounding at $20^{\circ} C$ . When power is switched off system cools from $t^{\circ} C$ to $(t / n)^{\circ} C$ in one minute. The heat capacity of the system is $1200 J /^{\circ} C$ . Find the limiting value of $n$ .

n \geq 100

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n \geq 55

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n \geq 60

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n \geq 75

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Solution

The correct option is C $n \geq 60$
We know that

$\frac{d Q}{d t} = - K (T - T_{0})$

Power, $P = 10 W$ ,

Temperature of the system $= 50^{\circ} C$ ,
Temperature of surrounding $= 20^{\circ} C$ ,
Heat capacity of the system

$= 1200 J /^{\circ} C$

$\frac{d Q}{d t} = K (50 - 20) = 10$

So, $k = 1 / 3$
Heat lost in $1$ minute $= Q$ ′

$\frac{d Q}{d t} \times 60 (J)$

$\frac{d Q}{d t} = \frac{1}{3} (t - 20)$

Fall in temperature $= t / n$

$c = \frac{Q^{'}}{Δ θ} = \frac{(\frac{1}{3}) \times (t - 20) \times 60}{(\frac{t}{n})}$

Putting values
$1200 = 20 n - \frac{400 n}{t}$

Since $t 0$ ,

so, $20 n > 1200$

$n \geq 60$

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