Question

At a constant pressure of \[ 2\times10^5\ \mathrm{Nm^{-2}}, \] if the volume of \(4\) moles of a monoatomic gas changes from \(1000\) cc to \(1500\) cc, then the change in internal energy of the gas is

• A. \(150\) J
• B. \(250\) J
• C. \(200\) J
• D. \(600\) J

Hint:

For a monoatomic ideal gas, \[ \boxed{\Delta U=\frac32nR\Delta T.} \] At constant pressure, \[ \boxed{nR\Delta T=P\Delta V,} \] so \[ \boxed{\Delta U=\frac32P\Delta V.} \]

Answer 1

The Correct Option is A

Step 1: Calculate the work done. Change in volume is \[ \Delta V = (1500-1000)\text{ cc} = 500\times10^{-6} = 5\times10^{-4}\text{ m}^3. \] Hence, \[ W = P\Delta V = 2\times10^5\times5\times10^{-4} = 100\text{ J}. \]

Step 2: Use the relation for a monoatomic gas. For a monoatomic ideal gas, \[ \Delta U = \frac32P\Delta V. \] Therefore, \[ \Delta U = \frac32\times100 = 150\text{ J}. \]

Step 3: Write the answer. Hence, \[ \boxed{150\text{ J}}. \] Thus, \[ \boxed{(A)} \] is the correct answer.