JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Heat & Thermodynamics

WhatsApp Email

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by : (

R =

universal gas constant)

(A) $\frac{M v ^{2}}{7 R}$
(B) $\frac{Mv ^{2}}{5 R}$ ✓ Correct
(C) $2 \frac{Mv ^{2}}{7 R}$
(D) $7 \frac{Mv ^{2}}{5 R}$

Answer: (B)

Solution

Given

γ = C_{P} / C_{V} = 1.4 = 1 + 2/ F

, we get

F = 5

(degrees of freedom). By energy conservation, the kinetic energy of the gas converts to internal energy:

\frac{1}{2} (nm) v^{2} = \frac{F}{2} n R Δ T

, where n is number of moles and m is mass per mole (M). This gives

Δ T = \frac{M v ^{2}}{F R} = \frac{M v ^{2}}{5 R}

JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Heat & Thermodynamics →

JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Heat & Thermodynamics

Solution

More JEE Main questions on Heat & Thermodynamics