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A vessel contains $14\,g$ of nitrogen gas at a temperature of $27^{\circ}\,C$. The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be $......J$ $\left(\right.$ Take $R =8.32\,J\,mol ^{-1} k ^{-1}$ )
Which of the following plots represents schematically the dependence of the time period of a pendulum, if measured and plotted as a function of the amplitude of its oscillations? (Note amplitude need not be small)
This question has Statement $- 1$ and Statement $-2$. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement $1$ : The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.
Statement $2$ : A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume.
Nitrogen gas is at $300^{\circ} C$ temperature. The temperature (in $K$) at which the $rms$ speed of a $H _{2}$, molecule would be equal to the $rms$ speed of a nitrogen molecule, is........
The temperature of a gas having $2.0 \times 10^{25}$ molecules per cubic meter at $1.38 \mathrm{~atm}$ (Given, $\mathrm{k}=$ $\left.1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)$ is :
$40$ calories of heat is needed to raise the temperature of $1\, mole$ of an ideal monoatomic gas from $20°C$ to $30°C$ at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume $(R = 2\,calorie\,mol{e^{ - 1}}{K^{ - 1}})$ is ..... $calorie$