Name: Wien's Displacement Law
Uploaded: 2019-07-19
Duration: 3 min 31 s
Description: Let's understand the relationship between the temperature of a blackbody and the wavelength at which the blackbody emits the most light. Let's learn about Wi...

Question

Explain variable state and steady state as heat flows through a bar. Describe Searle's method for determination of

K

.

Accepted Answer

Heat flow through a bar:

Let's consider an isotropic bar of the uniform area of the cross-section area $A$ as shown in the given below.

Fig: The isotropic uniform bar

Under the variable state, the temperature difference between two points is not constant, it varies with respect to time. The heat current is equal to the rate of flow of heat.

$H = \frac{d Q}{d t} = - K A \frac{d θ (x, t)}{d x} . . . . . . . . . . . . . (1)$

Under the steady-state, the temperature difference between the two points is constant.

So, $\frac{d θ}{d x} = constant$ , equation (1) becomes,

$\int_{0}^{L} H d x = - K A \int_{θ_{1}}^{θ_{2}} d θ H = \frac{Q}{t} = \frac{K A (θ_{1} - θ_{2})}{L} Q = \frac{K A (θ_{1} - θ_{2}) t}{L}$

Searle's method for determination of coefficient of thermal conductivity $(K)$ :

Searle's method is suitable for the determination of the absolute value of thermal conductivity of a material if it is available in the form of a rod.

Fig: Apparatus set up

The apparatus consists of a rod PQ, being properly insulated from the surrounding. The end P is heated by a steam chamber S. A copper pipe C is wound near the end Q. By injecting cold water at I, a steady flow of water is maintained within the copper pipe; and warm water leaves the pipe near exit E, which is collected. Two thermometer $T_{1} and T_{2}$ are fitted in the grooves, filled with mercury for good thermal contact. Two other thermometer $T_{3} and T_{4}$ are provided to measure the temperatures of cold water and warm water respectively.

The formula for the coefficient of thermal conductivity is given by,

$K = \frac{m (θ_{4} - θ_{3}) L}{A (θ_{1} - θ_{2}) t}$

Explain variable state and steady state as heat flows through a bar. Describe Searle's method for determination of $K$ .

Important Questions on Heat Transfer

Learn and Prepare for any exam you want !

Explain variable state and steady state as heat flows through a bar. Describe Searle's method for determination of K.

Important Questions on Heat Transfer

Learn and Prepare for any exam you want !

Explain variable state and steady state as heat flows through a bar. Describe Searle's method for determination of $K$ .