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

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Solution

Q.
If three moles of an ideal gas at 300 K expand isothermally from 30 ${dm}^{3}$ to 45 ${dm}^{3}$ against a constant opposing pressure of 80 kPa, then the amount of heat transferred is _____ J. [2024]

Ans.
(1200)

Work (W) against constant pressure is calculated as:

$W = - P_{ext} (V_{2} - V_{1}) = - 80 kPa \times (45 - 30) {dm}^{3}$

$= - 80 \times 1000 Pa \times 15 \times {(10^{- 1} m)}^{3}$

$= - 1200 J$

By first law of thermodynamics:

$Δ U = Q + W$

For isothermal process of an ideal gas, $Δ U = 0$

So, $Q = - W$

$Q = - (- 1200 J) = 1200 J$

Hence 1200 J of heat is absorbed in the process.

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