 Solution

Temperature describes thermal state and determines the direction of spontaneous heat transfer. A quantity of heat is energy transferred because of a temperature difference. It depends on the process and is measured in energy units; it is not another name for temperature. Equal heat inputs need not produce equal temperature rises in different masses or substances.

For a specified process, the specific heat capacity isOver a modest range with nearly constant $c$ and no phase change, $Q=mc\Delta T$. For a gas the constraint matters: heat capacity at constant pressure and heat capacity at constant volume generally differ because expansion can do work.

In method-of-mixtures calorimetry, a body of known mass $m_s$ at $T_s$ is transferred into water of mass $m_w$ at $T_w$ in a calibrated calorimeter initially also at $T_w$. If the final uniform temperature is $T_f$, the vessel and immersed fittings have heat capacity $C_{\mathrm{cal}}$, and losses are negligible,ThusStirring, quick transfer, a lid, a temperature-time record and allowance for surrounding heat exchange improve the inference. Ignoring the calorimeter's heat capacity systematically misattributes part of the energy uptake.

An alternative is electrical calorimetry: measure $E=\int VIdt$ supplied to a heater and compare the temperature rise with a blank or separately calibrated vessel. At nearly constant properties, $E=(mc+C_{\mathrm{cal}})\Delta T+Q_{\mathrm{loss}}$. An ice calorimeter instead measures the mass melted at a known phase-change temperature, using $Q=m_{\mathrm{melt}}{L}_f$ with appropriate corrections. Steam condensation similarly uses latent heat. These methods infer transferred energy from different measurable effects; a thermometer reading alone does not measure a quantity of heat.