Find the volume of \(1.20\,\mathrm{mol}\) of ideal gas at \(300\,\mathrm{K}\) and \(1.00\times10^5\,\mathrm{Pa}\).

A gas sample has \(p=2.0\times10^5\,\mathrm{Pa}\), \(V=3.0\times10^{-3}\,\mathrm{m^3}\), and \(T=290\,\mathrm{K}\). Find \(n\).

For a fixed amount of ideal gas at constant temperature, the volume is halved. What happens to the absolute pressure?

A fixed amount of ideal gas changes from \(p_1=100\,\mathrm{kPa}\), \(V_1=4.0\,\mathrm{L}\), \(T_1=300\,\mathrm{K}\) to \(V_2=2.5\,\mathrm{L}\), \(T_2=360\,\mathrm{K}\). Find \(p_2\).

Use \(pV=Nk_BT\) to find the number of molecules in a \(2.0\times10^{-3}\,\mathrm{m^3}\) gas sample at \(p=1.5\times10^5\,\mathrm{Pa}\) and \(T=300\,\mathrm{K}\).

An ideal gas has density \(\rho\), molar mass \(M\), pressure \(p\), and temperature \(T\). Derive \(\rho=pM/(RT)\).

A gas cylinder of volume \(0.080\,\mathrm{m^3}\) contains oxygen with molar mass \(3.2\times10^{-2}\,\mathrm{kg\,mol^{-1}}\) at \(280\,\mathrm{K}\) and \(5.0\times10^5\,\mathrm{Pa}\). Find the gas mass.

A fixed amount of ideal gas satisfies \(pV/T=\mathrm{constant}\). It is compressed to one third of its original volume while its Kelvin temperature doubles. Find \(p_2/p_1\).

A real gas is modeled by \(\left(p+a n^2/V^2\right)(V-nb)=nRT\). Explain what physical effects the \(a\) and \(b\) corrections represent, and state a condition under which the model reduces to \(pV=nRT\).

A fixed amount of ideal gas changes between two equilibrium states. Derive an expression for \(T_2\) in terms of \(p_1,V_1,T_1,p_2,V_2\), and state why gauge pressure cannot be used in this expression.

A sealed rigid tank contains ideal gas at \(p_1=2.4\times10^5\,\mathrm{Pa}\) and \(T_1=300\,\mathrm{K}\). The gas is heated to \(T_2=450\,\mathrm{K}\). Find the final absolute pressure.

For one mole of a van der Waals gas, \(\left(p+a/V_m^2\right)(V_m-b)=RT\). In the dilute limit \(V_m\gg b\), derive the first-order approximation \(p\approx RT/V_m+(RTb-a)/V_m^2\).

A gas has \(p=1.20\times10^5\,\mathrm{Pa}\), \(T=300\,\mathrm{K}\), and molar mass \(2.8\times10^{-2}\,\mathrm{kg\,mol^{-1}}\). Find its density using the ideal-gas model.

A gas obeys \(pV=nRT\). At fixed \(n\), pressure is increased by a factor of \(3\) while volume is reduced by a factor of \(2\). Find \(T_2/T_1\).

For one mole of a van der Waals gas, explain why the term \(V_m-b\) makes the pressure larger than the ideal-gas value at the same \(T\) and measured \(V_m\), if attractions are ignored.

Derive the ideal-gas density relation \(p=\rho RT/M\) and state the assumptions behind it.

A gas is described by \(pV=nRT\). Explain why the equation relates equilibrium states rather than every instant during a rapid compression.

Using \(pV=Nk_BT\), show that doubling molecule number at fixed \(V\) and \(T\) doubles pressure, and interpret microscopically.

In the van der Waals equation, explain why attractions reduce the measured wall pressure even though the correction is written as \(p+a n^2/V^2\).

A gas model gives \(pV/T\) constant for fixed amount. Explain two ways experimental data can reveal departure from ideal-gas behavior.