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(A) $A.$ According to Newton's law of cooling,the rate of loss of heat $\frac{dQ}{dt} \propto \Delta T$. If $\Delta T$ is doubled,the rate of loss of

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$A, B, C$ only

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(A) $A.$ According to Newton's law of cooling,the rate of loss of heat $\frac{dQ}{dt} \propto \Delta T$. If $\Delta T$ is doubled,the rate of loss of heat becomes twice. Thus,$A$ is correct.$B.$ The power radiated by a body is $P = \sigma e A T^4$. The ratio of radiation emitted is $\frac{H_P}{H_Q} = \left(\frac{T_P}{T_Q}\right)^4$. Converting temperatures to Kelvin: $T_P = 10 + 273 = 283 K$ and $T_Q = 20 + 273 = 293 K$. Thus,$\frac{H_P}{H_Q} = \left(\frac{283}{293}\right)^4 \approx (0.9658)^4 \approx 0.87$. However,using the approximation $\frac{293}{283} \approx 1.035$,then $(1.035)^4 \approx 1.15$. Thus,$1:1.15$ is correct. $B$ is correct.$C.$ Efficiency $\eta = 1 - \frac{T_L}{T_H} = 1 - \frac{100}{400} = 1 - 0.25 = 0.75$ or $75\%$. Thus,$C$ is correct.$D.$ Since $\frac{dQ}{dt} \propto \Delta T$,if $\Delta T$ is quadrupled,the rate of loss of heat becomes four times,not twice. Thus,$D$ is incorrect.Therefore,statements $A, B,$ and $C$ are correct.

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