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 $100K$ and $400K$ 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

Answer 1

Answer: (A)

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