Answer
410.1k+ views
Hint:The ability of a material to conduct heat is measured as thermal conductivity. The amount of heat flowing is directly proportional to the surface area, temperature difference, time period and inversely proportional to the thickness of the body. So, by using the formula of calculating the rate of flow of heat, we can find out the temperature gradient.
Complete step by step answer:
From the question, we know that the thermal conductivity of the material in CGS unit system is $k = 0.4\;{cal/^ \circ C} \cdot {\text{s}} \cdot {\text{cm}}$ and the rate of flow of heat per unit area, $\dfrac{{dQ}}{{Adt}} = 10cal/cm \cdot {s^2}$ .We know that the amount of rate of heat that flows across the body or material is expressed as,
$\dfrac{{dQ}}{{dt}} = - KA\dfrac{{dT}}{{dx}}$
Here, $A$ is the surface area of the material, $\dfrac{{dT}}{{dx}}$ is the temperature gradient, $T$ is the temperature and $x$ is the distance.
Rewrite the above equation, we have,
$\dfrac{{dQ}}{{Adt}} = - K\dfrac{{dT}}{{dx}}$ ,
Substitute the given values in the above equation, we get,
$
10 = - 0.4\dfrac{{dT}}{{dx}} \\
\Rightarrow \dfrac{{dT}}{{dx}} = - \dfrac{{10}}{{0.4}} \\
\therefore \dfrac{{dT}}{{dx}} = - 25^\circ C $
Here, a negative sign indicates that the fall in the temperature of the material with respect to distance.
Thus, the thermal gradient of the material is $25^\circ {\text{C/cm}}$ and option B is correct.
Note:In the formula of rate of flow of heat, the negative sign indicates the decrement of the temperature of the body along the positive x direction and $dt$ is expressed as${T_2} - {T_1}$ , where ${T_2}$ is final temperature and ${T_1}$ is initial temperature. The unit of thermal gradient in SI unit system is $J{s^{ - 1}}{m^{ - 1}}{K^{ - 1}}$ and in CI unit system is $cal \cdot {s^{ - 1}}c{m^{ - 1}}^\circ {C^{ - 1}}$ .
Complete step by step answer:
From the question, we know that the thermal conductivity of the material in CGS unit system is $k = 0.4\;{cal/^ \circ C} \cdot {\text{s}} \cdot {\text{cm}}$ and the rate of flow of heat per unit area, $\dfrac{{dQ}}{{Adt}} = 10cal/cm \cdot {s^2}$ .We know that the amount of rate of heat that flows across the body or material is expressed as,
$\dfrac{{dQ}}{{dt}} = - KA\dfrac{{dT}}{{dx}}$
Here, $A$ is the surface area of the material, $\dfrac{{dT}}{{dx}}$ is the temperature gradient, $T$ is the temperature and $x$ is the distance.
Rewrite the above equation, we have,
$\dfrac{{dQ}}{{Adt}} = - K\dfrac{{dT}}{{dx}}$ ,
Substitute the given values in the above equation, we get,
$
10 = - 0.4\dfrac{{dT}}{{dx}} \\
\Rightarrow \dfrac{{dT}}{{dx}} = - \dfrac{{10}}{{0.4}} \\
\therefore \dfrac{{dT}}{{dx}} = - 25^\circ C $
Here, a negative sign indicates that the fall in the temperature of the material with respect to distance.
Thus, the thermal gradient of the material is $25^\circ {\text{C/cm}}$ and option B is correct.
Note:In the formula of rate of flow of heat, the negative sign indicates the decrement of the temperature of the body along the positive x direction and $dt$ is expressed as${T_2} - {T_1}$ , where ${T_2}$ is final temperature and ${T_1}$ is initial temperature. The unit of thermal gradient in SI unit system is $J{s^{ - 1}}{m^{ - 1}}{K^{ - 1}}$ and in CI unit system is $cal \cdot {s^{ - 1}}c{m^{ - 1}}^\circ {C^{ - 1}}$ .
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)