Molecular oxygen having a mass of 10.0 g is in a cylinder...

Molecular oxygen having a mass of $10.0$ g is in a cylinder sealed with a movable piston. The gas is heated from $0.00^{\circ} \mathrm{C}$ to $10.0^{\circ} \mathrm{C}$ at a constant pressure and expands. Given that $c_{p}$ for $\mathrm{O}_{2}$ is $0.919$ $\mathrm{kJ} / \mathrm{kg}$, how much heat was received by the gas?

Key Concepts

Temperature Change and Unit Consistency

When calculating thermal energy changes, it is important to ensure that the temperature difference (?T) is measured consistently, often in Kelvin or degrees Celsius since the unit increment is the same. Additionally, the mass of the substance must be converted into appropriate units (such as kilograms) to match the units used for specific heat capacity.

Specific Heat Capacity at Constant Pressure (c?)

This is a thermodynamic property that describes the amount of heat required to raise the temperature of a unit mass of a substance by one degree while maintaining constant pressure. It is a crucial parameter in calorimetry and energy balance calculations in processes where pressure does not change.

Constant Pressure Process

In a constant pressure process, the pressure of the system remains fixed throughout the heating or cooling. Under these conditions, the heat added to or removed from the system is directly related to the change in the system's enthalpy, which simplifies the calculation of the thermal energy exchange.

Heat Transfer Calculation (Q = m·c?·?T)

This fundamental equation relates the heat transferred (Q) to the mass (m), the specific heat capacity at constant pressure (c?), and the temperature change (?T) of a substance. It forms the basis for solving calorimetric problems in thermodynamics, making it essential for analyzing energy transfer during heating or cooling under constant pressure.

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