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 10ºC and 20 ºC. 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 :

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A, B only

A, C only

A, B, C only

B, C, D only

answer is A.

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Detailed Solution

Heat Transfer

A. by Newton’s low of colling $\frac{dθ}{dt} =\propto ΔT$

B. $H = \frac{dθ}{dt} = σ {eAT}^{4} \Rightarrow \frac{H_{P}}{H_{Q}} = {(\frac{T_{P}}{T_{Q}})}^{4} = {(\frac{283}{293})}^{4}$

$H_{P} : H_{Q} = 1 (1 .03)^{4} = 1 : (1 .03)^{4} = 1 : 1 .15 \Rightarrow B is correct$

C. $η = 1 - \frac{100}{400} = \frac{3}{4} = 75 %$

D. is wrong as $\frac{dθ}{dt} \propto ΔT$

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