$A B C D E$ is a regular pentagon of uniform wire. The rate of heat entering at $A$ and leaving at $C$ is equal. If $T_{B}$ and $T_{D}$ are temperatures of $B$ and $D$ . Find the temperature of $C$ $(T_{C})$

\frac{3 T_{B} + 2 T_{D}}{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 T_{D} - 2 T_{B}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 T_{B} - 2 T_{D}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

can have any value

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $3 T_{D} - 2 T_{B}$

Let
$H_{1}$ be heat currents in section $A B C$
$H_{2}$ be heat currents in section $A E D C$
$R$ be the thermal resistance of each rod.

Thermal resistance of section $A B C$ is $2 R$ $(∵ two rods A B, B C are in series)$

Thermal resistance of section $A E D C$ is $3 R$
$(∵ three rods A E, E D, D C are in series)$

Then using thermal analogy of Ohms law

$T_{A} - T_{C} = 2 R H_{1} = 3 R H_{2}$
$\Rightarrow \frac{H_{1}}{H_{2}} = \frac{3}{2}$

also,
$T_{B} - T_{C} = R H_{1}$
$T_{D} - T_{C} = R H_{2}$

$\Rightarrow \frac{T_{B} - T_{C}}{T_{D} - T_{C}} = \frac{R H_{1}}{R H_{2}} = \frac{3}{2}$

$\Rightarrow T_{C} = 3 T_{D} - 2 T_{B}$

Suggest Corrections

Similar questions

ABCDE is a regular pentagon of uniform wire. The rate of heat entering at A and leaving at C is equal.
$T_{B}$ and $T_{D}$ are temperature of B and D. Find the temperature $T_{C}$

Q. Six identical conducting rods having uniform cross-section area are fixed to make a regular hexagon as shown. The ends A and C are maintained at constant temperature

2 T_{0}

and

6 T_{0}

. After the steady state is reached, pick up the correct relation between temperatures

T_{B}, T_{D}, T_{E}

and

T_{F}

of ends B, D, E and F respectively :
(Neglect convection and radiation losses)

A conducting tube is passing through a bath. A liquid at temperature $90^{\circ} C$ and specific heat s is entering at one end of tube. The rate of flow of liquid is 1kg/s and exit temperature is $50^{\circ} C$ . In bath another liquid having specific heat 2s and inlet temperature $20^{\circ} C$ is entering at a rate of 2kg/s. If the exit temperature of liquid coming out of the bath is 10x. Find x (Assume steady-state condition) ___

Q. Magnetic field strength at the centre of regular pentagon made of a conducting wire of uniform cross section area as shown in figure is : (i amount of current enters at A and leaves at E)

Q. Four points charges, each having a charge q are placed on the four corners A, B, C and D of a regular pentagon

A B C D E

. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon.

Join BYJU'S Learning Program

ABCDE is a regular pentagon of uniform wire. The rate of heat entering at A and leaving at C is equal. If TB and TD are temperatures of B and D. Find the temperature of C (TC)

$A B C D E$ is a regular pentagon of uniform wire. The rate of heat entering at $A$ and leaving at $C$ is equal. If $T_{B}$ and $T_{D}$ are temperatures of $B$ and $D$ . Find the temperature of $C$ $(T_{C})$