As 3.0 liters of ideal gas at 27^∘ C is heated, it expands at a constant pressure of 2.0 atm. Ho

step 1 Hello and welcome to this video solution of numerate. So there are 3 liters of ideal gas at 27 d

As 3.0 liters of ideal gas at 27^∘ C is heated, it expands...

As $3.0$ liters of ideal gas at $27^{\circ} \mathrm{C}$ is heated, it expands at a constant pressure of $2.0$ atm. How much work is done by the gas as its temperature is changed from $27^{\circ} \mathrm{C}$ to $227^{\circ} \mathrm{C}$ ?

Key Concepts

Temperature Conversion

Temperature conversion is a key concept when working with thermodynamic equations because temperatures must be measured on an absolute scale. It involves converting degrees Celsius to Kelvin by adding 273.15, ensuring that calculations with the ideal gas law are accurate.

Work in Thermodynamics

In thermodynamics, the work done by a gas during expansion or compression is defined as the integral of pressure with respect to volume change. For processes at constant pressure, this simplifies to work being equal to the product of pressure and the change in volume (W = P?V).

Unit Conversion

Unit conversion ensures that all quantities in a thermodynamic calculation are in compatible units. For example, pressure, volume, and temperature must be expressed in units that correspond correctly with the gas constant used, and this may involve converting pressure from atmospheres to the appropriate unit or volume from liters to cubic meters.

Ideal Gas Law

This law relates the pressure, volume, temperature, and number of moles of an ideal gas using the equation PV = nRT. It allows us to understand how changes in one variable, such as temperature, affect another variable, like volume, when pressure is held constant.

Isobaric Process

An isobaric process is one in which the pressure remains constant. During such a process, if the temperature of an ideal gas increases, the gas expands, and the work done by the gas can be computed as the product of the constant pressure and the change in volume.

Transcript

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