10 mole of oxygen is heated at constant volume from 30°C$30^{\circ}\text{C}$ to 40°C$40^{\circ}\text{C}$. The change in the internal energy of the gas is ____ cal. (The molecular specific heat of oxygen at constant pressure, Cₚ = 7 cal./mol °C$C_{p} = 7\text{ cal./mol }^{\circ}\text{C}$ and R = 2 cal./mol °C$R = 2\text{ cal./mol }^{\circ}\text{C}$.)
Numerical Answer Type:
Enter a numerical valueAnswer: 500 to 500+4 marks
Solution & Explanation
Related Formula
Δ U = n Cv Δ T$$\Delta U = n C_v \Delta T$$
Cv = Cₚ - R$C_v = C_p - R$
Core Logic
Given values:
n = 10 moles$n = 10\text{ moles}$Δ T = 40°C - 30°C = 10°C$\Delta T = 40^{\circ}\text{C} - 30^{\circ}\text{C} = 10^{\circ}\text{C}$Cₚ = 7 cal/mol·°C$C_p = 7\text{ cal/mol}\cdot^{\circ}\text{C}$R = 2 cal/mol·°C$R = 2\text{ cal/mol}\cdot^{\circ}\text{C}$
Δ U = n Cv Δ T$$\Delta U = n C_v \Delta T$$Δ U = 10 × (7 - 2) × (40 - 30)$$\Delta U = 10 \times (7 - 2) \times (40 - 30)$$Δ U = 10 × 5 × 10 = 500 cal$$\Delta U = 10 \times 5 \times 10 = 500\text{ cal}$$
Pattern Recognition
Change in internal energy of an ideal gas is ALWAYS Δ U = n Cv Δ T$\Delta U = n C_v \Delta T$, regardless of the process (constant volume or not). Use Cv = Cₚ - R$C_v = C_p - R$ when Cₚ$C_p$ is given.
Chapter Mix
Class 11 Physics: Thermodynamics
Class 11 Physics: Kinetic Theory of Gases
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.
