Question

Calculate the constant external pressure required to compress \(4\) moles of an ideal gas, from volume \(30\) dm\({}^{3}\) to \(20\) dm\({}^{3}\) when the work obtained is \(4053\) J.

• A. \(4\) atm.
• B. \(4.5\) atm.
• C. \(5\) atm.
• D. \(3.5\) atm.

Hint:

Use w = -P times delta V, convert the work from joules to litre atmosphere and solve for P.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
For compression at constant external pressure, \(w = -P_{ext}\,\Delta V\).
Work done on the gas is positive.

Step 2: Find the Volume Change
\(\Delta V = 20 - 30 = -10\ \text{dm}^3 = -10\ \text{L}\)

Step 3: Convert the Work
\(w = 4053\ \text{J}\) and \(1\ \text{L atm} = 101.3\ \text{J}\).
So \(w = \dfrac{4053}{101.3} = 40\ \text{L atm}\).

Step 4: Calculation
\(40 = -P(-10)\), so \(P = \dfrac{40}{10} = 4\ \text{atm}\).

Final Answer:
The required external pressure is 4 atm. \[ \boxed{\text{(A) }4\ \text{atm}} \]