Certain amount of an ideal gas is contained in a closed vessel. The vessel is moving with a constant velocity v. The molecular mass of gas is M. The rise in temperature of the gas when the vessel is suddenly stopped is (γ=CP / CV)

Question

Certain amount of an ideal gas is contained in a closed vessel. The vessel is moving with a constant velocity v. The molecular mass of gas is M. The rise in temperature of the gas when the vessel is suddenly stopped is (&gamma;=CP / CV) (A) (M v2(&gamma;-1)/2 R(&gamma;+1)) (B) (M v2(&gamma;-1)/2 R) (C) (M v2/2 R(&gamma;+1)) (D) (M v2/2 R(&gamma;-1))

Tardigrade Admin · Accepted Answer

If m is the total mass of the gas, then its kinetic energy =1 / 2 m v2. When the vessel is suddenly stopped, total kinetic energy will increase the temperature of the gas (because process will be adiabatic), i.e., (1/2) m v2=μ Cv Δ T=(m/M) Cv Δ T ⇒ (m/M) (R/&gamma;-1) Δ T=(1/2) m v2 ( text As Cv=(R/&gamma;-1)) ⇒ Δ T=(M v2(&gamma;-1)/2 R)

Q. Certain amount of an ideal gas is contained in a closed vessel. The vessel is moving with a constant velocity $v$ . The molecular mass of gas is $M$ . The rise in temperature of the gas when the vessel is suddenly stopped is $(γ = C_{P} / C_{V})$

$\frac{M v ^{2} ( γ - 1 )}{2 R ( γ + 1 )}$

$\frac{M v ^{2} ( γ - 1 )}{2 R}$

$\frac{M v ^{2}}{2 R ( γ + 1 )}$

$\frac{M v ^{2}}{2 R ( γ - 1 )}$

Q. Certain amount of an ideal gas is contained in a closed vessel. The vessel is moving with a constant velocity v. The molecular mass of gas is M. The rise in temperature of the gas when the vessel is suddenly stopped is (γ=CP​/CV​)

2R(γ+1)Mv2(γ−1)​

2RMv2(γ−1)​

2R(γ+1)Mv2​

2R(γ−1)Mv2​

Q. Certain amount of an ideal gas is contained in a closed vessel. The vessel is moving with a constant velocity $v$ . The molecular mass of gas is $M$ . The rise in temperature of the gas when the vessel is suddenly stopped is $(γ = C_{P} / C_{V})$

$\frac{M v ^{2} ( γ - 1 )}{2 R ( γ + 1 )}$

$\frac{M v ^{2} ( γ - 1 )}{2 R}$

$\frac{M v ^{2}}{2 R ( γ + 1 )}$

$\frac{M v ^{2}}{2 R ( γ - 1 )}$