The Question is from neet-physics thermodynamics , and it was created by the author Mr. ANIL KUMAR.G

Question

Two different metallic rods of the same length have their ends kept at the same temperatures $	heta_1$ and $	heta_2$ with $	heta_2 > 	heta_1$. If $A_1$ and $A_2$ are their cross-sectional areas, $K_1$ and $K_2$ their thermal conductivities, the rate of heat flow is the same in both the rods.  The condition for this is:

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
	**Primary Concept**: Heat Conduction
	**Related Topics**: Thermal Conductivity, Rate of Heat Flow
	**Prerequisites**: Understanding of heat transfer by conduction, definition of thermal conductivity.
## SOLUTION PATHWAY
**Given Information**:
	* Two rods of the same length (let's call it 'L').
	* Ends of both rods are at temperatures $	heta_1$ and $	heta_2$.
	* Cross-sectional areas are $A_1$ and $A_2$.
	* Thermal conductivities are $K_1$ and $K_2$.
	* Rate of heat flow (Q/t) is the same for both rods.
	* $	heta_2 > 	heta_1$.
**Method & Steps**:
	1.	Write the formula for the rate of heat flow through a rod:
		Reasoning: The rate of heat flow through a material is proportional to the area, the temperature difference, and inversely proportional to the length. The proportionality constant is the thermal conductivity.
		Formula/Rule: $Q/t = \frac{KA(	heta_2 - 	heta_1)}{L}$
	2.	Apply the formula to both rods:
		Working: For rod 1: $(Q/t)_1 = \frac{K_1 A_1 (	heta_2 - 	heta_1)}{L}$. For rod 2: $(Q/t)_2 = \frac{K_2 A_2 (	heta_2 - 	heta_1)}{L}$.
		Key Point: Since the rate of heat flow is the same in both rods, we have $(Q/t)_1 = (Q/t)_2$.
	3.	Equate the two expressions and simplify:
		Result: $\frac{K_1 A_1 (	heta_2 - 	heta_1)}{L} = \frac{K_2 A_2 (	heta_2 - 	heta_1)}{L}$. Canceling the common terms $(	heta_2 - 	heta_1)$ and $L$ from both sides, we get $K_1 A_1 = K_2 A_2$.
		Verification: The derived condition matches the correct answer option.
 ## OPTION ANALYSIS
[A] ✓: The condition $K_1A_1 = K_2A_2$ ensures that the rate of heat flow is the same for both rods, as derived from the heat conduction equation.
[B] :x: The condition $K_1A_2 = K_2A_1$ is not consistent with the heat conduction equation. It would imply the ratio of conductivity to area is the same, not the product.
[C] :x: The condition $K_1/A_1 = K_2/A_2$ is not consistent with the heat conduction equation. It implies the ratio of conductivity to area is the same, not the product.
[D] :x: The condition $A_1/A_2=K_1/K_2$ or $K_2A_1=K_1A_2$ is not consistent with the heat conduction equation. It would imply inverse relation between conductivity and area.
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Confusing the formula for heat flow. Remember that heat flow is proportional to the product of area and thermal conductivity and inversely proportional to the length.
		2.[Error 2]: Incorrectly canceling terms in the equation. Ensure that terms are canceled only when they are common to both sides of the equation.
	**Quick Tips**:
		1.[Helpful shortcut]: When dealing with problems involving rate of heat flow, always start by writing the basic formula $Q/t = \frac{KA(	heta_2 - 	heta_1)}{L}$ and then apply the given conditions.
		2.[Memory aid]: Remember the heat flow equation by thinking of it as 'rate is proportional to conductivity, area, and temperature difference, and inversely proportional to length'.

Mr. ANIL KUMAR.G · Answer

The correct Option is "K₁A₁ = K₂A₂"

Mr. ANIL KUMAR.G · Answer

K₁A₂ = K₂A₁

Mr. ANIL KUMAR.G · Answer

K₁/A₁ = K₂/A₂

Mr. ANIL KUMAR.G · Answer

A₁/A₂=K₁/K₂

NEET Physics Thermodynamics MCQs

Select Topic

Question Tags

Question Tags

NEET Subjects

Our Bots

Company