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: Energy balance:
Temperature stays fixed, so the gas has the same internal energy at the start and end. All the work done on it by the surroundings must leave as heat.

Step 2: Numbers:
Work done on gas = pressure $\times$ volume decrease = $4\text{ bar}\times 15\text{ dm}^3 = 60\text{ bar dm}^3$.
Since 1 bar dm$^3$ = 100 J, this is 6000 J = 6.0 kJ.
Heat released = work received = 6.0 kJ, which is option (D).

Final Answer:
The system releases 6.0 kJ of heat. \[ \boxed{6.0\text{ kJ}} \]