Question

If three moles of an ideal gas at 300 K expand isothermally from 30 dm³ to 45 dm³ against a constant opposing pressure of 80 kPa, then the amount of heat transferred is ______ J.

Answer 1

Correct Answer: 1200

The heat transferred during an isothermal expansion of an ideal gas is calculated using the work done formula for such processes: \( W = -P_{\text{ext}} \times \Delta V \). The external pressure \( P_{\text{ext}} \) is given as 80 kPa, equivalent to 80,000 Pa. The change in volume \( \Delta V \), calculated as \( V_f - V_i \), is 45 dm³ - 30 dm³ = 15 dm³, which is 0.015 m³.
Substituting these values into the work formula yields:
\( W = -80,000 \times 0.015 = -1,200 \) J.
According to the first law of thermodynamics, \( \Delta U = Q + W \). In an isothermal process, the internal energy change \( \Delta U \) is zero since the temperature remains constant. Therefore, the equation simplifies to \( 0 = Q + W \), meaning \( Q = -W \).
Consequently, the heat transferred \( Q \) is 1,200 J.