The balloon in the preceding problem starts at a pressure of 100 kPa and rises to an altitude wh

step 1 This question belongs to the laws of thermodynamics in which we have number of moles and equals

The balloon in the preceding problem starts at a pressure of...

The balloon in the preceding problem starts at a pressure of $100 \mathrm{kPa}$ and rises to an altitude where the pressure is $75 \mathrm{kPa}$ maintaining a constant $300 \mathrm{~K}$ temperature. (a) By what factor does its volume increase? (b) How much work does the gas do?

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Key Concepts

Thermodynamic Work

In an isothermal process for an ideal gas, the work done by or on the gas is calculated by integrating the pressure with respect to volume, yielding the expression W = nRT ln(V2/V1). This formula shows that the work done depends on the logarithm of the volume ratio, which can also be expressed in terms of the pressure ratio due to the constant temperature condition.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant throughout. In such processes for an ideal gas, the product of pressure and volume remains constant (PV = constant). This is a key property that allows one to relate initial and final states through the equation P1V1 = P2V2.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, is a fundamental relation in thermodynamics that connects the pressure, volume, and temperature of an ideal gas with the amount (in moles) and the gas constant. It provides a baseline for understanding how gases respond to changes in thermodynamic variables, particularly in processes where one of the parameters, such as temperature in an isothermal process, remains constant.

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