Question

The pressure of a gas changes linearly with volume from $A$ to $B$ as shown in figure If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be Is

 

• A. $4.5 J$
• B. $-4.5 J$
• C. zero
• D. $6 J$

Hint:

For an ideal gas undergoing a process with no heat exchange, the change in internal energy is equal to the work done by or on the gas.

Answer 1

The Correct Option is A

As $\Delta q=0$
$\Delta u=-W$
$W=\int PdV$
$\Delta u=-W=30\times 10^3\times 150\times 10^{-6}$
$=4500\times 10^{-3}$
$=4.5J$

Answer 2

As there is no heat exchange (\( \Delta q = 0 \)), the change in internal energy is equal to the work done by the gas:

\[ \Delta u = - W \]

The work done by the gas is given by:

\[ W = \int P \, dV \]

Since the pressure changes linearly, we can use the average pressure to calculate the work done:

\[ W = P_{\text{avg}} \times \Delta V = 30 \times 10^3 \times 150 \times 10^{-6} = 4500 \times 10^{-3} = 4.5 \, \text{J} \]

Thus, the change in internal energy is \( 4.5 \, \text{J} \).