Question

Calculate the quantity of heat released from system when 2 moles of and ideal gas compressed isothermally from volume \(25\text{ dm}^3\) to \(10\text{ dm}^3\) at constant external pressure 4 bar.

• A. \(5\cdot 5\text{ kJ}\)
• B. \(5\cdot 0\text{ kJ}\)
• C. \(6\cdot 5\text{ kJ}\)
• D. \(6\cdot 0\text{ kJ}\)

Hint:

For an ideal gas at constant temperature the internal energy does not change, so q = -w.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The compression is isothermal, and for an ideal gas the internal energy depends only on temperature. So \(\Delta U = 0\) and the first law gives \(q = -w\).

Step 2: Key Formula or Approach:
Work done on the gas against a constant external pressure: \(w = -p_{ex}(V_2 - V_1)\).
Use 1 bar \(\times\) 1 dm\(^3\) = 100 J.

Step 3: Detailed Explanation:
\(V_2 - V_1 = 10 - 25 = -15\) dm\(^3\).
\[ w = -4\times(-15) = +60\text{ bar dm}^3 = 60\times 100 = 6000\text{ J} = +6.0\text{ kJ} \]
The sign is positive, so 6.0 kJ of work is done on the system. Since \(\Delta U = q + w = 0\):
\[ q = -6.0\text{ kJ} \]
The negative sign means 6.0 kJ of heat is released by the system. The number of moles (2) is not needed because the pressure is constant and the volumes are given.

Final Answer:
Heat released is 6.0 kJ, option (D). \[ \boxed{6.0\text{ kJ}} \]