An insulated container is filled with ice at $0\,^oC$ , and another container is filled with water that is continuously boiling at $100\,^oC$ . In series of experiments, the containers are connected by various thick metal rods that pass through the walls of container as shown in the figure
In the experiment $I$ : a copper rod is used and all ice melts in $20$ minutes.
In the experiment $II$ : a steel rod of identical dimensions is used and all ice melts in $80$ minutes.
In the experiment $III$ : both the rods are used in series and all ice melts in $t_{10}$ minutes.
In the experiment $IV$ : both rods are used in parallel and all ice melts in $t_{20}$ minutes.
Diffcult
Download our app for free and get started
$\mathrm{P}_{1}=\frac{\mathrm{K}_{1} \mathrm{A}(100-0)}{\mathrm{L}} \Rightarrow Q=\mathrm{P}_{1} \mathrm{t}_{1}$
$\mathrm{P}_{2}=\frac{\mathrm{K}_{2} \mathrm{A}(100-0)}{\mathrm{L}} \Rightarrow \mathrm{Q}=\mathrm{P}_{2} \mathrm{t}_{2}$
$\mathrm{P}_{3}=\frac{\mathrm{P}_{1} \mathrm{P}_{2}}{\mathrm{P}_{1}+\mathrm{P}_{2}}=\frac{\frac{\mathrm{Q}}{\mathrm{t}_{1}} \times \frac{\mathrm{Q}}{\mathrm{t}_{2}}}{\frac{\mathrm{Q}}{\mathrm{t}_{1}}+\frac{\mathrm{Q}}{\mathrm{t}_{2}}}=\frac{\mathrm{Q}}{\mathrm{t}_{1}+\mathrm{t}_{2}}$
$\Rightarrow Q=P_{3}\left(t_{1}+t_{2}\right)$
$\Rightarrow \mathrm{t}_{10}=\mathrm{t}_{1}+\mathrm{t}_{2}=100 \mathrm{minutes}$
$\mathrm{P}_{2}=\mathrm{P}_{1}+\mathrm{P}_{2}=\frac{\mathrm{Q}}{\mathrm{t}_{1}}+\frac{\mathrm{Q}}{\mathrm{t}_{2}}=\frac{\mathrm{Q}\left(\mathrm{t}_{1}+\mathrm{t}_{2}\right)}{\mathrm{t}_{1} \mathrm{t}_{2}}$
$\Rightarrow Q=P_{4}\left(\frac{t_{1} t_{2}}{t_{1}+t_{2}}\right)$
$\Rightarrow \mathrm{t}_{20}=\frac{\mathrm{t}_{1} \mathrm{t}_{2}}{\mathrm{t}_{1}+\mathrm{t}_{2}}=\frac{20 \times 80}{100}=16 \mathrm{min}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1If the temperature of the sun were to be increased from $T$ to $2T$ and its radius from $R$ to $2R$ , then the ratio of the radiant energy received on the earth to what it was previously will beView Solution
- 2Two different rods $A$ and $B$ are kept as shown in figure. The ratio of thermal conductivities of $A$ and $B$ isView Solution
- 3Calculate radiation power for sphere whose temperature is $227^{\circ} C$ and radius $2\, m$ and emissivity $0.8$ (in $W$)View Solution
- 4A body takes $10\, minutes$ to cool from $60\,^oC$ to $50\,^oC$. The temperature of surroundings is constant at $25\,^oC$. Then, the temperature of the body after next $10\, minutes$ will be approximately ....... $^oC$View Solution
- 5In a certain planetary system, it is observed that one of the celestial bodies having a surface temperature of $200 \;K$, emits radiation of maximum intensity near the wavelength $12\; \mu m$. The surface temperature (in $K$) of a nearby star which emits light of maximum intensity at a wavelength $\lambda= 4800\;\mathring A$ isView Solution
- 6$Assertion :$ A tube light emits white light.View Solution
$Reason :$ Emission of light in a tube takes place at a very high temperature. - 7View SolutionWhich of the following is more closed to a black body?
- 8View SolutionA block of metal is heated to a temperature much higher than the room temperature and allowed to cool in a room free from air currents. Which of the following curves correctly represents the rate of cooling
- 9View SolutionA body, which emits radiations of all possible wavelengths, is known as ...........
- 10Two different rods $A$ and $B$ are kept as shown in figure. The variation of temperature of different cross sections is plotted in a graph shown in figure. The ratio of thermal conductivities of $A$ and $B$ isView Solution
