A solid maintained at t1° C is kept in an evacuated chamber at temperature t2° C (t2 gg t1). The rate of heat absorbed by the body is proportional to

Question

A solid maintained at t1° C is kept in an evacuated chamber at temperature t2° C (t2 gg t1). The rate of heat absorbed by the body is proportional to (A) t24 - t41  (B) (t24 +273) - (t41 +273) (C) t2 - t1 (D) t22 - t12

Tardigrade Admin · Accepted Answer

As we know that, the rate of cooling is

\frac{d θ}{d t} = b A (θ - θ_{0})

where,

b A =

constant

\Rightarrow \frac{d θ}{d t} \propto θ - θ_{0}

Also

- \frac{d T}{d t} \propto T - T_{0}

where,

T =

temperature
and

t =

time
So, the rate of heat absorbed by cooled body is proportional to

t_{2} - t_{1}

.

Q. A solid maintained at $t_{1}^{\circ} C$ is kept in an evacuated chamber at temperature $t_{2}^{\circ} C$ $(t_{2} ≫ t_{1})$ . The rate of heat absorbed by the body is proportional to

$t_{2}^{4} - t_{1}^{4}$

$(t_{2}^{4} + 273) - (t_{1}^{4} + 273)$

$t_{2} - t_{1}$

$t_{2}^{2} - t_{1}^{2}$

Q. A solid maintained at t1∘​C is kept in an evacuated chamber at temperature t2∘​C (t2​≫t1​). The rate of heat absorbed by the body is proportional to

t24​−t14​

(t24​+273)−(t14​+273)

t2​−t1​

t22​−t12​

As we know that, the rate of cooling is dtdθ​=bA(θ−θ0​) where, bA= constant ⇒dtdθ​∝θ−θ0​ Also −dtdT​∝T−T0​ where, T= temperature and t= time So, the rate of heat absorbed by cooled body is proportional to t2​−t1​.

Q. A solid maintained at $t_{1}^{\circ} C$ is kept in an evacuated chamber at temperature $t_{2}^{\circ} C$ $(t_{2} ≫ t_{1})$ . The rate of heat absorbed by the body is proportional to

$t_{2}^{4} - t_{1}^{4}$

$(t_{2}^{4} + 273) - (t_{1}^{4} + 273)$

$t_{2} - t_{1}$

$t_{2}^{2} - t_{1}^{2}$