One gram mole of oxygen is enclosed in a vessel at a temperature of $27$ and at one atmospheric pressure. The vessel is thermally insulated and is moved with a constant speed $u_{0}$ . Calculate $u_{0}$ if the rise in temperature is $1 K$ when the vessel is suddenly stopped?

35.6 m / s

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45 m / s

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90 m / s

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60 m / s

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Solution

The correct option is B $45 m / s$

since internal energy depends only on the temperature ,
as the temperature changes,
the change in internal energy is

$Δ U = \frac{n f R Δ T}{2}$

vessel contains a gas of mass M,
change in kinetic energy $= \frac{n M v^{2}}{2}$

$\frac{n f R Δ T}{2}$ = $\frac{n M v^{2}}{2}$

$\frac{2}{\frac{c_{p}}{c_{v}} - 1}$

$f = \frac{2}{\frac{2}{5}}$ = 5

putting value

$v = 45 m / s$

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One gram mole of oxygen is enclosed in a vessel at a temperature of 27 and at one atmospheric pressure. The vessel is thermally insulated and is moved with a constant speed u0. Calculate u0 if the rise in temperature is 1K when the vessel is suddenly stopped?

The correct option is B 45m/ssince internal energy depends only on the temperature ,as the temperature changes,the change in internal energy is ΔU=nfRΔT2vessel contains a gas of mass M,change in kinetic energy =nMv22nfRΔT2= nMv22 2cpcv−1f=225 = 5putting value v=45m/s

One gram mole of oxygen is enclosed in a vessel at a temperature of $27$ and at one atmospheric pressure. The vessel is thermally insulated and is moved with a constant speed $u_{0}$ . Calculate $u_{0}$ if the rise in temperature is $1 K$ when the vessel is suddenly stopped?