A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats . It is moving with speed and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by:

Question

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats $γ$ . It is moving with speed $v$ and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by:

Smart Achievers · Accepted Answer

(3)

As, work done is zero.

So, loss in kinetic energy = heat gain by the gas

$\frac{1}{2} m v^{2} = n C_{v} Δ T = n \frac{R}{γ - 1} Δ T$

$\frac{1}{2} m v^{2} = \frac{m}{M} \frac{R}{γ - 1} Δ T$

$∴$ $Δ T = \frac{M v^{2} (γ - 1)}{2 R} K$

Solution

Q.
A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats $γ$ . It is moving with speed $v$ and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by:

1 $\frac{(γ - 1)}{2 γ R} M v^{2} K$

2 $\frac{γ M^{2} v}{2 R} K$

3 $\frac{(γ - 1)}{2 R} M v^{2} K$

4 $\frac{(γ - 1)}{2 (γ + 1) R} M v^{2} K$

Ans.
(3)

As, work done is zero.

So, loss in kinetic energy = heat gain by the gas

$\frac{1}{2} m v^{2} = n C_{v} Δ T = n \frac{R}{γ - 1} Δ T$

$\frac{1}{2} m v^{2} = \frac{m}{M} \frac{R}{γ - 1} Δ T$

$∴$ $Δ T = \frac{M v^{2} (γ - 1)}{2 R} K$

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Solution

Q. A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats γ. It is moving with speed v and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by:

1 (γ-1)2γRMv2K

2 γM2v2RK

3 (γ-1)2RMv2K

4 (γ-1)2(γ+1)RMv2K

Ans. (3) As, work done is zero. So, loss in kinetic energy = heat gain by the gas 12mv2=nCvΔT=nRγ-1ΔT 12mv2=mMRγ-1ΔT ∴ ΔT=Mv2(γ-1)2RK