First Law of Thermodynamics (rate form):
\(\dfrac{dU}{dt} = \dfrac{dQ}{dt} - \dfrac{dW}{dt}\)
Where: dQ/dt = rate of heat supplied = 100 W (into system)
dW/dt = rate of work done BY system = 75 J/s
Calculate rate of internal energy increase:
\(\dfrac{dU}{dt} = 100 - 75 = \mathbf{25 \text{ W}}\) ✓
Physical interpretation:
Of the 100 J of heat entering the system every second, 75 J/s leaves as work done by the system. The remaining 25 J/s stays in the system as increased internal energy (temperature rise).
The First Law of Thermodynamics is a statement of energy conservation for thermodynamic systems. It states that the change in internal energy of a system equals the heat added to the system minus the work done by the system:
\(\Delta U = Q - W\) (Physics convention)
\(\Delta U = Q + W\) (Chemistry convention: W = work done ON system)
In NEET (and this problem), the physics convention is used: Q is heat added to system (positive if absorbed), W is work done by system (positive if system expands). The first law essentially says energy cannot be created or destroyed — only converted between forms.
Dividing by time dt: dU/dt = dQ/dt − dW/dt. This gives the power form — all terms are in watts (J/s). This is exactly what this problem uses: heat supply rate (100 W) minus work rate (75 W) = internal energy rate (25 W).
📌 Isothermal: T = const → ΔU = 0 → Q = W (ideal gas)
📌 Adiabatic: Q = 0 → ΔU = −W (work done at expense of internal energy)
📌 Isochoric: V = const → W = 0 → ΔU = Q (all heat goes to internal energy)
📌 Isobaric: P = const → W = PΔV, ΔU = Q − PΔV
Internal energy U is the sum of kinetic and potential energies of all molecules in the system. For an ideal gas: U = nCᵥT (depends only on temperature). For real gases, U also depends on volume (due to intermolecular forces). When U increases, temperature rises (for ideal gas). Internal energy is a state function — depends only on current state, not on how it was reached.
W = ∫P dV (general)
📌 Isobaric: W = PΔV = P(V₂−V₁)
📌 Isothermal: W = nRT ln(V₂/V₁)
📌 Adiabatic: W = (P₁V₁−P₂V₂)/(γ−1) = nCᵥ(T₁−T₂)
📌 Isochoric: W = 0 (no volume change)
Cᵥ = heat capacity at constant volume = ΔU/ΔT per mole. Cₚ = heat capacity at constant pressure > Cᵥ (extra energy for PΔV work). Relation: Cₚ − Cᵥ = R (Mayer's relation). Ratio γ = Cₚ/Cᵥ: monoatomic gas (5/3 ≈ 1.67), diatomic (7/5 = 1.4), triatomic (4/3 ≈ 1.33).
⚠️ Physics convention: ΔU = Q − W (W = work by system)
⚠️ Chemistry convention: ΔU = Q + W (W = work on system)
⚠️ NEET uses physics convention — be consistent throughout!
⚠️ Heat into system: Q positive. Work by system: W positive.