Question

An ideal gas expands along the path AB as shown in the p-V diagram. The work done is

• A. $4 \times 10^4$ J
• B. $1.2 \times 10^5$ J
• C. $2.4 \times 10^5$ J
• D. None of these

Hint:

An ideal gas expands along the path AB as shown in the p-V diagram. The work done is

Answer 1

The Correct Option is B

To find the work done by an ideal gas during expansion along the path AB on the p-V diagram, we use the concept of work done in thermodynamics, which is given by the area under the curve on a p-V diagram.

Since the path AB is a straight line, the process is linear, and we can calculate the work done using the average pressure. The initial and final pressures and volumes are:

• Initial pressure, \(P_A = 4 \, \text{Pa}\)
• Final pressure, \(P_B = 8 \, \text{Pa}\)
• Initial volume, \(V_A = 0.3 \, \text{m}^3\)
• Final volume, \(V_B = 0.5 \, \text{m}^3\)

The work done by the gas is given by:

\(W = \frac{1}{2} \times (P_A + P_B) \times (V_B - V_A)\)

Substituting the values, we get:

\(W = \frac{1}{2} \times (4 + 8) \, \text{Pa} \times (0.5 - 0.3) \, \text{m}^3\)

\(W = \frac{1}{2} \times 12 \, \text{Pa} \times 0.2 \, \text{m}^3\)

\(W = \frac{1}{2} \times 2.4 \, \text{J} \times 10^5\)

\(W = 1.2 \times 10^5 \, \text{J}\)

Thus, the work done during the expansion is \(1.2 \times 10^5 \, \text{J}\).

The correct answer is $1.2 \times 10^5$ J.