Answer

Verified

348.3k+ views

**Hint :**Entropy of the system is defined as the randomness or degree of freedom of any system. Entropy is denoted by ‘S’. Entropy is a thermodynamic quantity which depends on thermodynamic variables that are temperature, pressure and volume. We cannot calculate the absolute value of entropy for any system but we can calculate the change in entropy

( $ \Delta S $ ).

**Complete Step By Step Answer:**

Thermodynamically change in entropy is represented as

$ \Delta S = \dfrac{{{q_{reversible}}}}{T} $ . This is the formula to calculate change in entropy.

Where,

$ {q_{reversible}} $ = heat exchange for the system which is reversible in nature (Joule or calorie).

$ T $ = temperature(K).

The unit of entropy is $ J{K^{ - 1}} $ or $ Cal{K^{ - 1}} $ .

$ 1J{K^{ - 1}} $ is said to be 1 entropy unit.

Given: $ \Delta S $ =?

n=1mol

T= $ {27^0}C $ = $ 27 + 273 = 300K $ .

$ {V_1} = 2L $

$ {V_2} = 20L $

Let’s consider $ R = 2calmo{l^{ - 1}}{K^{ - 1}} $

Let’s rewrite the equation,

$ \Delta S = \dfrac{{{q_{reversible}}}}{T} $

Substituting q by $ \Delta U + P\Delta V $ ,

$ \Delta S = \dfrac{{\Delta U + P\Delta V}}{T} $

For an ideal gas $ \Delta T = 0,\Delta U = 0 $ .

So, we get

$ \Delta S = \dfrac{{P\Delta V}}{T} $

From the ideal gas equation we know that $ P = \dfrac{{nrT}}{V} $

$ \Delta S = \dfrac{{nRT}}{{V \times T}} \times \Delta V $

$ \Delta S = nR\dfrac{{\Delta V}}{V} $

On integration we have,

$ \Delta S = nR\ln \dfrac{{{V_2}}}{{{V_1}}} $ .

Substituting the given values we have,

$ \Rightarrow \Delta S = 1 \times 2 \times \ln \dfrac{{20}}{2} $

$ \Delta S = 2 \times 2.303 $

$ \Delta S = 4.606cal{K^{ - 1}}mo{l^{ - 1}} $ .

**So, the correct option is (B).**

**Note :**

For any reversible system there is one and only path. So we can say that $ {q_{reversible}} $ is a state function. Change in entropy is inversely proportional to temperature that is at low

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Guru Purnima speech in English in 100 words class 7 english CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Select the word that is correctly spelled a Twelveth class 10 english CBSE