Read the following statements:

$A.$ When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice.

$B.$ Two bodies $P$ and $Q$ having equal surface areas are maintained at temperature $10^{\circ}\,C$ and $20^{\circ}\,C$. The thermal radiation emitted in a given time by $P$ and $Q$ are in the ratio $1: 1.15$

$C.$ A carnot Engine working between $100\,K$ and $400\,K$ has an efficiency of $75 \%$

$D.$ When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.

Choose the correct answer from the options given below :

Q: Read the following statements: $A.$ When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice. $B.$ Two bodies $P$ and $Q$ having equal surface areas are maintained at temperature $10^{\circ}\,C$ and $20^{\circ}\,C$. The thermal radiation emitted in a given time by $P$ and $Q$ are in the ratio $1: 1.15$ $C.$ A carnot Engine working between $100\,K$ and $400\,K$ has an efficiency of $75 \%$ $D.$ When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below :

a Heat Transfer A. by Newton's low of colling $\frac{d \theta}{d t}=\propto \Delta T$ B. $H =\frac{d \theta}{d t}=\sigma e AT ^{4} \Rightarrow \frac{ H _{ P }}{ H _{Q}}=\left(\frac{ T _{ P }}{ T _{Q}}\right)^{4}=\left(\frac{283}{293}\right)^{4}$ $H _{ p }: H _{ Q }=1(1.03)^{4}=1:(1.03)^{4}=1: 1.15$ $\Rightarrow B$ is correct C. $\eta=1-\frac{100}{400}=\frac{3}{4}=75 \%$ D. is wrong as $\frac{d \theta}{d t} \propto \Delta T$

Question

Read the following statements:

$A.$ When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice.

$B.$ Two bodies $P$ and $Q$ having equal surface areas are maintained at temperature $10^{\circ}\,C$ and $20^{\circ}\,C$. The thermal radiation emitted in a given time by $P$ and $Q$ are in the ratio $1: 1.15$

$C.$ A carnot Engine working between $100\,K$ and $400\,K$ has an efficiency of $75 \%$

$D.$ When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.

Choose the correct answer from the options given below :

A$A, B, C $ only
B$A, B$ only
C$A, C$ only
D$B, C, D$ only

JEE MAIN 2022, Diffcult

Column $-\,I$	Column $-\,II$
$(a)$ Wein's constant	$(i)$ $Wm^{-2}\,K^{-4}$
$(b)$ Stefan-Boltzmaan's constant.	$(ii)$ $Wm^{-1}\,K^{4}$
	$(iii)$ $mK$

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