An insulated box has a barrier that confines a gas to only one side of the box. the barrier springs a leak, allowing the gas to flow and occupy both sides of the box. which statement best describes the entropy of this system? a) the entropy is greater in the first state, with all the gas on one side of the box. b) the entropy is greater in the second state, with the gas on both sides of the box. c) the entropy is the same in both states, since no heat was added to the gas and its temperature did not change.

B) The entropy is greater in the second state, with the gas on both sides of the box.

Explanation:

As we know that ,this is a irreversible process .The process leaves some effect on the surrounding or on the system itself ,is known as irreversible process.But on the other hand those process does not leave any effect on the system and surrounding is known as reversible process.

The entropy in the irreversible process always increases ,that is why the the entropy will be more when gas occupy the both boxes.

Therefore the answer is --B

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .