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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, B, C $ only
$A, B$ only
$A, C$ only
$B, C, D$ only
Solution
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 $\frac{d \theta}{d t} \propto \Delta T$
