A vertical cylinder with a massless piston is filled with...

A vertical cylinder with a massless piston is filled with one mole of an ideal gas. The piston can move freely without friction. The piston is slowly raised so that the gas expands isothermally at temperature $300 \mathrm{~K}$. The amount of work done in increasing the volume two times is $R=\frac{25}{3} \mathrm{~J} / \mathrm{mol} / \mathrm{K}, \log _{\mathrm{e}} 2=0.7$ (A) $1750 \mathrm{~J}$ (B) $2500 \mathrm{~J}$ (C) $750 \mathrm{~J}$ (D) $4250 \mathrm{~J}$

A vertical cylinder with a massless piston is filled with one mole of an ideal gas. The piston can move freely without friction. The piston is slowly raised so that the gas expands isothermally at temperature $300 \mathrm{~K}$. The amount of work done in increasing the volume two times is $R=\frac{25}{3} \mathrm{~J} / \mathrm{mol} / \mathrm{K}, \log _{\mathrm{e}} 2=0.7$
(A) $1750 \mathrm{~J}$
(B) $2500 \mathrm{~J}$
(C) $750 \mathrm{~J}$
(D) $4250 \mathrm{~J}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Natural Logarithm

The natural logarithm (ln) is a logarithm to the base e, where e is approximately 2.71828. The natural logarithm appears in the expression for the work done during an isothermal process due to the integration of the inverse relationship between pressure and volume.

Ideal Gas Law

The ideal gas law, given by PV = nRT, relates the pressure (P), volume (V), and temperature (T) of an ideal gas with the number of moles (n) and the gas constant (R). This fundamental equation is used to describe how gases behave under different conditions and is critical when analyzing processes such as expansions and compressions.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant. For an ideal gas undergoing an isothermal expansion or compression, this means that any work done by or on the system is balanced by heat transfer, keeping the internal energy constant.

Work Calculation in Isothermal Processes

In an isothermal process involving an ideal gas, the work done by the gas is calculated using the integral of pressure with respect to volume, leading to the formula W = nRT ln(V_final/V_initial). This equation highlights the logarithmic relationship between the volumes and the work done during the process.

Please give Ace some feedback