Explanation
It is given that $$U={{U}_{0}}V$$
For a diatomic molecule, internal energy is given by
$$ U=\dfrac{5}{2}nRT $$
$$ {{U}_{0}}V=\dfrac{5}{2}nRT $$
Taking derivative on both sides.
$$ {{U}_{0}}\dfrac{dV}{dT}=\dfrac{5}{2}R n $$
$$ {{C}_{v}}=\dfrac{5}{2}R\,\,\,\,\,(\because \dfrac{{{U}_{0}}dU}{ndT}={{C}_{v}}) $$
Hence, molar heat capacity is $$[\dfrac{5}{2}R]$$.
The temperature of a gas is due to
When the volume of a gas is decreased at constant temperature the pressure increases because the molecules
The graph between temperature and pressure of a perfect gas is
The graph drawn between pressure and temperature at constant volume for a given mass of different molecular weights $$M_{1}$$ and $$M_{2}$$ are the straight lines as shown in the figure then
At constant pressure, density of a gas is :
Hint: Density of a substance is given by $$\rho = \dfrac{m}{V}$$ , where $$m$$is the mass of the substance and $$V$$ is its volume.
Correction Option: B
Explanation for correct option:
$$ \Rightarrow PV \alpha nRT$$
$$ \Rightarrow PV = \dfrac{m}{M} RT$$, where $$m$$ and $$M$$ are weight and molecular weight of the gas.
$$ \Rightarrow P = \dfrac{m}{V}\dfrac{{RT}}{M}$$
Here, $$\rho = \dfrac{m}{V}$$ and $$R' = \dfrac{R}{M}$$, where $$R'$$ is the specific gas constant for the gas.
$$ \Rightarrow P = \rho R'T$$
$$ \Rightarrow \rho = \dfrac{P}{{R'T}}$$
$$\therefore \rho \alpha \dfrac{1}{T}$$
Hence, at constant pressure, density of a gas is inversely proportional to absolute temperature.
Universal gas constant per molecule is called
All gasses deviate from gas laws at
If the slope of P-T graph for a given mass of a gas increases, then the volume of the gas
An ideal gas is that which
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In a gas equation, PV = RT, V refers to the volume of:
The relation between volume V, pressure P and absolute temperature T of an ideal gas is PV = xT, where x is a constant. The value of x depend upon
The density of an ideal gas
Choose the only correct statement from the following
If pressure and temperature of an ideal gas are doubled and volume is halved, the number of molecules of the gas
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