10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from P₁$\mathrm{P}_{1}$ to P₂$\mathrm{P}_{2}$ is α$\alpha$ Joule ( P₁ = 21.7Pa$\mathrm{P}_{1} = 21.7\mathrm{Pa}$ and P₂ = 30Pa$\mathrm{P}_{2} = 30\mathrm{Pa}$ , Cv = 21J / K.mol$\mathrm{C}_{\mathrm{v}} = 21\mathrm{J / K.mol}$ , R = 8.3J / mol.K$R = 8.3\mathrm{J / mol.K}$ ). The value of α$\alpha$ is ____.
A Pressure-Volume graph displaying an isochoric rise from P1 to P2 at constant V=1.
A.24$24$
B.15$15$
C.21$21$
D.28$28$
Solution & Explanation
Related Formula
Δ Q = n Cv Δ T$$\Delta Q = n C_v \Delta T$$
From Ideal Gas Law for Isochoric Process:
n R Δ T = Δ P · V$$n R \Delta T = \Delta P \cdot V$$
Core Logic
From the P-V graph, the process from P₁$P_1$ to P₂$P_2$ takes place at a constant volume V = 1 m³$V = 1 \text{ m}^3$.
For constant volume processes, Δ Q$\Delta Q$ strictly scales with Δ P$\Delta P$. Re-writing n Δ T$n \Delta T$ as V Δ P / R$V \Delta P / R$ circumvents calculating absolute temperatures entirely.
Keywords:#heat involved in the process#JEE Main 2026 Evening Q43#Thermodynamics JEE Main 2026#Isochoric Process and Heat Transfer JEE Main 2026#P-V graph#Isochoric process#Thermodynamic cycle#Ideal gas
More Thermodynamics Previous-Year Questions — Page 8
Qjee_main_2024_31_jan_morningIsobaric Process
The given figure represents two isobaric processes for the same mass of an ideal gas, then
A Volume vs Temperature (V-T) graph showing two straight lines starting from the origin representing distinct constant pressures P1 and P2.
A.P₂≥ P₁$\mathrm{P}_2\geq \mathrm{P}_1$
B.P₂ > P₁$\mathrm{P}_2 > \mathrm{P}_1$
C.P₁ = P₂$\mathrm{P_1 = P_2}$
D.P₁ > P₂$\mathrm{P}_1 > \mathrm{P}_2$
Solution
Related Formula
PV = nRT$PV = nRT$
Core Logic
From the Ideal Gas Law:
V = ((nR)/(P)) T$$V = \left(\frac{nR}{P}\right) T$$
In a V-T$V-T$ graph, the equation of the line represents y = mx$y = mx$, where the slope m$m$ is:
Practice past-year questions one chapter at a time. Pick an exam → subject → chapter and get every PYQ for that topic — pulled together from all past papers — with the chapter's key formulas alongside.
