Question

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it. (1) If both assertion and reason and the reason is the correct explanation of the Assertion. (2) If both assertion and reason are true but reason is not the correct explanation of the assertion. (3) If the assertion is true but reason is false. (4) If the assertion and reason both are false. Assertion: When a gas is allowed to expand, work done by gas is positive. Reason: Force due to gaseous pressure and displacement (of position) on in the same direction. (A) 1 (B) 2 (C) 3 (D) 4

Short answer

(A) 1

Step-by-step solution

Understand the Assertion statement

When a gas is allowed to expand, work done by the gas is positive. This statement refers to the process of a gas expanding due to its pressure. We need to check if the work done in this process is positive.

Understand the Reason statement

Force due to gaseous pressure and displacement (of position) on in the same direction. This statement explains the reason behind the positive work done by the gas during expansion. The force due to gaseous pressure and the displacement of the gas particles must be in the same direction for the work done to be positive.

Determine if Assertion and Reason are true

The Assertion is true because when a gas is allowed to expand, it exerts force on its surroundings (e.g., the walls of a container) that ultimately results in positive work done. The Reason is also true, as the force exerted by the gas is in the same direction as the displacement of the gas particles, leading to positive work done.

Determine if Reason is the correct explanation of Assertion

The Reason indeed explains the Assertion correctly because the positive work done by the expanding gas is due to the force exerted by the gas and the displacement of the gas particles being in the same direction. This means that option 1 is the correct answer.

Choose the correct option

Since we found that both Assertion and Reason statements are true and the Reason statement provides the correct explanation for the given Assertion, we should choose option (A) 1 as our answer.

Key concepts

Work Done by Gas

In thermodynamics, when a gas expands against an external pressure, it is said to perform work. Imagine a gas inside a piston; as it pushes the piston outward, it spends energy. This energy expenditure is what we refer to as "work done by gas."
Remember that work done (W) is defined by the formula: \[ W = P \Delta V \] where \( P \) is the pressure exerted by the gas and \( \Delta V \) is the change in volume. In simpler terms, if a gas pushes against a piston, making it move outward, the work done is positive because the gas is losing energy to its surroundings while doing this work.
You might wonder why it's positive. When work is done on the system, the system gains energy. Conversely, when the system does work on the surroundings, it loses energy, thus, work done is considered positive. This sign convention helps us nicely describe the expansion process and energy transformation in the gas.

Gas Expansion

Gas expansion is a fundamental concept in thermodynamics. It occurs when gas molecules spread out to occupy more volume, typically due to a decrease in external pressure or an increase in temperature. Let’s break down the expansion process:

• When gas particles gain energy, they move faster and tend to spread out.
• This spreading out can happen because of heating or from lowering the surrounding pressure.
• The outcome is an increase in the volume that the gas occupies.

A real-world example of gas expansion is when you heat the air inside a balloon. The air molecules move more vigorously and thus require more space, causing the balloon to inflate. Understanding gas expansion is crucial, especially when studying how gases behave under various pressures and temperatures.

Force and Displacement Direction

The direction of force and displacement plays a pivotal role in determining if the work done is positive. When a gas expands, it exerts a force outward against whatever is confining it, like the walls of a container or a piston.

• The force exerted by the gas is due to pressure, a result of gas molecules colliding with each other and the container walls.
• During expansion, since the gas pushes outward, the gas causes a displacement in the same direction as the force.
• This alignment of force and displacement directions makes the work done by the gas positive.

Conceptually, think of it like this: if you push a book across a table, the direction of your push and the book's motion are the same. This is similar to how gas expansion works, ensuring that work done in such scenarios maintains a positive value for thermodynamic calculations.