Answer

Verified

47.4k+ views

**Hint:**Use the formula of the volume coefficient of expansion given below, and substitute the value of the temperature and the volume before expansion and after expansion in it. The simplification of the obtained equation provides the answer.

**Formula used:**

The formula of the volume coefficient of expansion is given by

$\alpha = \dfrac{{{V_2} - {V_1}}}{{{V_1}{t_2} - {V_2}{t_1}}}$

Where $\alpha $ is the volume coefficient of expansion, ${V_2}$ is the volume of the gas after expansion, ${V_1}$ is the volume of the gas before expansion, ${t_1}$ is the first temperature of the gas and ${t_2}$ is the second temperature of the gas.

**Complete step by step solution**

It is given that the

Initial volume of the gas, ${V_1} = 1000\,cc$

Final volume of the gas, ${V_2} = 1200\,cc$

Initial temperature of the gas, ${t_1} = {27^ \circ }\,C$

Final temperature of the gas, ${t_2} = {87^ \circ }\,C$

By using the formula of the volume coefficient of expansion,

$\alpha = \dfrac{{{V_2} - {V_1}}}{{{V_1}{t_2} - {V_2}{t_1}}}$

Substituting the values of the initial and the final temperature and also the initial and the final volume of the gas.

$\alpha = \dfrac{{1200 - 1000}}{{\left( {1000 \times 87} \right) - \left( {1200 \times 27} \right)}}$

By simplifying the above equation, we get

$\alpha = \dfrac{{200}}{{87000 - 32400}}$

By doing basic arithmetic operation, we get

$\alpha = \dfrac{{200}}{{54600}}$

By further simplification,

$\alpha = \dfrac{1}{{273}}{\,^0}\,{C^{ - 1}}$

Hence the value of the coefficient of expansion is obtained as $\dfrac{1}{{273}}{\,^0}\,{C^{ - 1}}$ .

**Thus the option (A) is correct.**

**Note:**The basic concept behind this question is the gas molecules occupy greater space on heating. Hence when the temperature increases, the volume occupied by the gas also increases. This is because heating causes the molecules in the gas to move further apart.

Recently Updated Pages

To get a maximum current in an external resistance class 1 physics JEE_Main

f a body travels with constant acceleration which of class 1 physics JEE_Main

A hollow sphere of mass M and radius R is rotating class 1 physics JEE_Main

If the beams of electrons and protons move parallel class 1 physics JEE_Main

Two radioactive nuclei P and Q in a given sample decay class 1 physics JEE_Main

silver wire has diameter 04mm and resistivity 16 times class 12 physics JEE_Main

Other Pages

Choose the correct statements A A dimensionally correct class 11 physics JEE_Main

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

The force of interaction of two dipoles if the two class 12 physics JEE_Main

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main