P-V Work & Sign Conventions
Stop losing marks to negative signs. Master the IUPAC Chemistry sign conventions for Heat ($q$) and Work ($w$), compute Pressure-Volume work, and conquer the First Law of Thermodynamics.
Module Focus
The biggest trap in Thermodynamics is the sign convention. Chemistry and Physics use completely opposite sign conventions for Work. If you apply a Physics formula in a Chemistry exam, your answer will have the wrong sign, and the examiner always includes both the positive and negative values in the options. This module firmly establishes the IUPAC Chemistry standards.
1. IUPAC Sign Conventions (Chemistry)
In Chemistry, the System is our primary focus. We view energy changes from the perspective of the system's "bank account." If energy enters the system, it's a deposit (Positive). If energy leaves the system, it's a withdrawal (Negative).
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+
$q$ is Positive: Heat is absorbed by the system from the surroundings (Endothermic process). Energy is added.
-
-
$q$ is Negative: Heat is released by the system to the surroundings (Exothermic process). Energy is lost.
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+
$w$ is Positive: Work is done ON the system by the surroundings (Compression). Energy is added to the gas.
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-
$w$ is Negative: Work is done BY the system on the surroundings (Expansion). The gas uses its own energy to push out.
In Physics, work done by the system (expansion) is considered positive because the force and displacement are in the same direction. Forget this in Chemistry. In Chemistry (IUPAC), expansion is ALWAYS negative work ($w < 0$).
2. Pressure-Volume (P-V) Work
Mechanical work in chemistry usually involves a gas expanding or compressing against an external pressure ($P_{ext}$). The formula for work done is derived to naturally fit the IUPAC sign convention.
The Universal Work Formula
Formula gives: $w = -(+)(+) = \mathbf{\text{Negative}}$.
(Work done BY the system)
Formula gives: $w = -(+)(-) = \mathbf{\text{Positive}}$.
(Work done ON the system)
In most numericals, Pressure is given in atm or bar, and Volume in Litres (L). The calculated work will be in L·atm. You MUST convert this to Joules (J) to use it in equations with heat.
$1 \text{ L}\cdot\text{bar} = 100 \text{ Joules}$
Free Expansion (Expansion in Vacuum)
If a gas expands into a vacuum, there is no opposing external pressure ($P_{ext} = 0$). Since $w = -P_{ext}\Delta V$, the work done during free expansion is always ZERO, regardless of whether the process is isothermal or adiabatic, reversible or irreversible.
3. First Law of Thermodynamics
The Law of Conservation of Energy. It states that the energy of an isolated system is constant. The mathematical formulation directly links internal energy ($U$) with heat ($q$) and work ($w$).
Applying the Law under specific conditions:
- Isochoric Process (Constant Volume): $\Delta V = 0 \Rightarrow w = 0$.
Therefore, $\mathbf{\Delta U = q_v}$. (Heat exchanged at constant volume equals change in internal energy). - Adiabatic Process: $q = 0$.
Therefore, $\mathbf{\Delta U = w_{ad}}$. (If work is done by the gas, $\Delta U$ is negative, so temperature drops/gas cools). - Isothermal Process (Ideal Gas): $\Delta T = 0 \Rightarrow \Delta U = 0$.
Therefore, $0 = q + w \Rightarrow \mathbf{q = -w}$. (Heat absorbed by the gas is entirely used to do expansion work).
4. Work done in Reversible vs Irreversible Processes
The formula $w = -P_{ext}\Delta V$ is specifically for Irreversible (constant external pressure) processes.
Reversible Isothermal Expansion
In a reversible process, the external pressure is not constant; it is always infinitesimally smaller than the gas pressure ($P_{ext} = P_{gas} - dP$). Integrating this gives the formula:
(Remember: For expansion $V_2 > V_1$, the log term is positive, making $w$ negative, perfectly satisfying the IUPAC convention.)
Area under the P-V Curve
The magnitude of work done is given by the Area under the P-V graph projected onto the Volume (x) axis.
- Cyclic Process (Clockwise): Represents a net expansion. In Chemistry, expansion work is negative. Therefore, $\mathbf{w_{\text{cycle}} = \text{Negative Area}}$.
- Cyclic Process (Anticlockwise): Represents a net compression. In Chemistry, compression work is positive. Therefore, $\mathbf{w_{\text{cycle}} = \text{Positive Area}}$.
NEET Grand Test: P-V Work & First Law
15 High-Order Thinking Questions testing IUPAC conventions, Free Expansion, and cyclic signs.
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