Answer
405k+ views
Hint:Consider the definitions of the heat capacity and specific heat capacity to derive a relation between them. Apply the given condition and find the ratio of specific heats of A and B.
Complete step by step answer:
Heat capacity: It is a measurable quantity that gives the amount of heat required to raise the temperature of a body by one degree Celsius. Now for heat capacity, heat supplied to a body/absorbed by a body is proportional to the corresponding change in temperature.
$
\Delta Q \propto \Delta T \\
\Rightarrow\Delta Q = C\Delta T \\
\Rightarrow C = \dfrac{{\Delta Q}}{{\Delta T}} \\
$
Here, $C$ is heat capacity.
Specific heat capacity: It is a measurable quantity that gives the amount of heat required to raise the temperature of the body of unit mass by one degree Celsius. For Specific heat capacity, heat supplied to a body/absorbed by a body is proportional to mass of the body and corresponding change in temperature.
$
\Rightarrow \Delta Q \propto m \\
\Rightarrow\Delta Q \propto \Delta T \\
\Rightarrow \Delta Q \propto m\Delta T \\
\Rightarrow \Delta Q = ms\Delta T \\
$
Here, $s$ is the specific heat.
Now, if you compare, the ratio of heat absorbed by the body and corresponding change in temperature is $\dfrac{{\Delta Q}}{{\Delta T}}$ which should be the same since they represent the same quantity. Hence you can equate both the values of the ratio obtained.
$\therefore C = ms$
Now, given that the heat capacity is the same for both the materials.
${m_A}{s_A} = {m_B}{s_B}$ and we have$m = \rho V$
$
\Rightarrow {\rho _A}{V_A}{s_A} = {\rho _B}{V_B}{s_B} \\
\Rightarrow\dfrac{{{s_A}}}{{{s_B}}} = \dfrac{{{\rho _B}{V_B}}}{{{\rho _A}{V_A}}} \\
\Rightarrow\dfrac{{{s_A}}}{{{s_B}}} = \dfrac{{2000 \times 12}}{{1500 \times 8}} \\
\therefore\dfrac{{{s_A}}}{{{s_B}}} = 2 \\
$
Therefore, the ratio of specific heats of A and B will be $2:1$.Hence, option (D) is correct.
Note: Always keep in mind the difference between heat capacity and specific heat capacity. Although in definition of both the quantities we used the unit of temperature as Celsius, in equation we use the unit of temperature as Kelvin.
Complete step by step answer:
Heat capacity: It is a measurable quantity that gives the amount of heat required to raise the temperature of a body by one degree Celsius. Now for heat capacity, heat supplied to a body/absorbed by a body is proportional to the corresponding change in temperature.
$
\Delta Q \propto \Delta T \\
\Rightarrow\Delta Q = C\Delta T \\
\Rightarrow C = \dfrac{{\Delta Q}}{{\Delta T}} \\
$
Here, $C$ is heat capacity.
Specific heat capacity: It is a measurable quantity that gives the amount of heat required to raise the temperature of the body of unit mass by one degree Celsius. For Specific heat capacity, heat supplied to a body/absorbed by a body is proportional to mass of the body and corresponding change in temperature.
$
\Rightarrow \Delta Q \propto m \\
\Rightarrow\Delta Q \propto \Delta T \\
\Rightarrow \Delta Q \propto m\Delta T \\
\Rightarrow \Delta Q = ms\Delta T \\
$
Here, $s$ is the specific heat.
Now, if you compare, the ratio of heat absorbed by the body and corresponding change in temperature is $\dfrac{{\Delta Q}}{{\Delta T}}$ which should be the same since they represent the same quantity. Hence you can equate both the values of the ratio obtained.
$\therefore C = ms$
Now, given that the heat capacity is the same for both the materials.
${m_A}{s_A} = {m_B}{s_B}$ and we have$m = \rho V$
$
\Rightarrow {\rho _A}{V_A}{s_A} = {\rho _B}{V_B}{s_B} \\
\Rightarrow\dfrac{{{s_A}}}{{{s_B}}} = \dfrac{{{\rho _B}{V_B}}}{{{\rho _A}{V_A}}} \\
\Rightarrow\dfrac{{{s_A}}}{{{s_B}}} = \dfrac{{2000 \times 12}}{{1500 \times 8}} \\
\therefore\dfrac{{{s_A}}}{{{s_B}}} = 2 \\
$
Therefore, the ratio of specific heats of A and B will be $2:1$.Hence, option (D) is correct.
Note: Always keep in mind the difference between heat capacity and specific heat capacity. Although in definition of both the quantities we used the unit of temperature as Celsius, in equation we use the unit of temperature as Kelvin.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science 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)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology 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)
Write a letter to the principal requesting him to grant class 10 english 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)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)