Question

Two metallic blocks M₁ and M₂ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M₂ is K then the thermal conductivity of M₁ will be ______. [Assume steady state heat conduction]

Options

• 10 K

• 8 K

• 12.5 K

• 2 K

Answer 1

Two metallic blocks M₁ and M₂ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M₂ is K then the thermal conductivity of M₁ will be 8 K. [Assume steady state heat conduction]

Explanation:

As Q = constant in series

So, Q_M1 = Q_M2 

⇒ `(100-80)/(16/"k"_1"A")=(80-0)/(8/"k"_2"A") [∵ "Q" = ("T"_1-"T"_2)/("l"/"kA")]`

⇒ `20/16xx"k"_1"A"=80/8"k"_2"A"`

⇒ `"k"_2=(20xx8)/(16xx80)"k"_1`

⇒ `"k"_2 = "k"_1/8`

⇒ k₁ = 8k₂ = 8k.