What is the change in internal energy for 0.5 moles of an ideal gas heated from 260 K to 310 K at constant volume? ( C_v
**First law applications** for isobaric W = P ΔV, Q = n C_p ΔT, ΔU = n C_v ΔT, for isothermal ideal gas ΔU=0 Q=W=n R T ln(V₂/V₁), for adiabatic Q=0 W= -ΔU = (P₁V₁ - P₂V₂)/(γ-1), for isochoric W=0 ΔU=Q=n C_v ΔT, enabling calculation of Q,W,ΔU for any process. Δ U = μ C_v Δ T . μ = 0.5 , C_v = 20.8 , Δ T = 310 - 260 = 50 . Δ U = 0.5 × 20.8 × 50 = 520 J . Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P ΔV,
Ref: NCERT > Physics Book > Thermodynamics > First Law of Thermodynamics Applications