1. Tardigrade
  2. Question
  3. Physics
  4. 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° C and 20 ° 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 :

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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 :

JEE MainJEE Main 2022Thermal Properties of Matter

Solution:

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