A fifteen-watt heater is used to heat a monatomic ideal gas...

A fifteen-watt heater is used to heat a monatomic ideal gas at a constant pressure of
$7.60 \times 10^{5}$ Pa. During the process, the $1.40 \times 10^{-3} \mathrm{m}^{3}$ volume of the
gas increases by 25.0$\% .$ How long was the heater on?

Key Concepts

Isobaric Process

An isobaric process is one in which the pressure remains constant while other state variables, such as volume and temperature, change. This concept is important in understanding how systems exchange energy in the form of work (calculated as pressure times the change in volume) during expansion or compression.

Work Done in Thermodynamic Processes

In thermodynamics, work represents the energy transferred when the system undergoes a change in volume under a constant pressure. It is calculated as the product of the pressure and the change in volume (W = p?V), making it a central concept in processes where gases expand or contract.

First Law of Thermodynamics

The first law of thermodynamics, which is essentially the conservation of energy, relates the change in the internal energy of a system to the heat added to the system and the work done by the system (?U = Q - W). This principle is critical when analyzing energy flows during processes such as heating or expansion.

Ideal Gas Law

The ideal gas law (PV = nRT) provides a relationship between a gas's pressure, volume, temperature, and the number of moles present. It is fundamental in calculating changes in state variables for ideal gases during thermal processes, including those conducted at constant pressure.

Power and Energy Relation

Power, measured in watts, is the rate at which energy is transferred or converted, with one watt equal to one joule per second. This concept links the total energy provided by a device, such as a heater, to the duration of its operation, allowing for calculations of energy input over time.

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