Convert \(27.0\,{}^\circ\mathrm{C}\) to kelvins.

A fixed-volume gas thermometer has pressure \(80.0\,\mathrm{kPa}\) at \(250\,\mathrm{K}\). Find the pressure at \(500\,\mathrm{K}\).

A fixed-volume gas thermometer pressure increases from \(1.00\times10^5\,\mathrm{Pa}\) to \(1.25\times10^5\,\mathrm{Pa}\). By what factor does the Kelvin temperature change?

A fixed-volume gas thermometer reads \(94.0\,\mathrm{kPa}\) at \(273.15\,\mathrm{K}\). What Kelvin temperature corresponds to \(110\,\mathrm{kPa}\)?

A fixed-volume gas has pressure \(120\,\mathrm{kPa}\) at \(20.0\,{}^\circ\mathrm{C}\). Find its pressure at \(80.0\,{}^\circ\mathrm{C}\).

A student says doubling the Celsius temperature of a fixed-volume gas doubles its pressure. Use \(20\,{}^\circ\mathrm{C}\) and \(40\,{}^\circ\mathrm{C}\) as a counterexample.

A fixed-volume gas thermometer is calibrated at \(273.15\,\mathrm{K}\), where its pressure is \(101\,\mathrm{kPa}\). It is then placed in a bath and reads \(75.0\,\mathrm{kPa}\). Find the bath temperature in kelvins and Celsius.

Two fixed-volume gas thermometers contain different amounts of gas. Thermometer A reads \(60\,\mathrm{kPa}\) at \(300\,\mathrm{K}\), while thermometer B reads \(150\,\mathrm{kPa}\) at \(300\,\mathrm{K}\). At an unknown temperature their pressures are \(72\,\mathrm{kPa}\) and \(180\,\mathrm{kPa}\). Show that they give the same temperature.

A fixed-volume gas thermometer has pressure \(p_C\) at \(0\,{}^\circ\mathrm{C}\). Derive the pressure expected at \(T_C\) in Celsius, assuming ideal gas-thermometer behavior.

A constant-volume thermometer has a small pressure offset, so the measured pressure is \(p_{\mathrm{meas}}=aT+b\), where \(T\) is the true Kelvin temperature and \(b\ne0\). Using two calibration temperatures \(T_1,T_2\) and measured pressures \(p_1,p_2\), derive \(T\) for a later measured pressure \(p\).