A gas is contained in a cylinder and expands according to...

A gas is contained in a cylinder and expands according to the relation $P V^{1.3}=$ constant. The initial pressure and initial volume of the gas is $30 \mathrm{~atm}$ and $30 \mathrm{~mm}^{3}$ respectively. If the final pressure is $15 \mathrm{~atm}$, then the work done on the face of piston by the pressure force of the gas, is : (a) $5 \times 10^{i} \mathrm{~J}$ (b) $4.35 \times 10^{4} \mathrm{~J}$ (c) $3 \times 10^{4} \mathrm{~J}$ (d) $4 \times 10^{4} \mathrm{~J}$

A gas is contained in a cylinder and expands according to the relation $P V^{1.3}=$ constant. The initial pressure and initial volume of the gas is $30 \mathrm{~atm}$ and $30 \mathrm{~mm}^{3}$ respectively. If the final pressure is $15 \mathrm{~atm}$, then the work done on the face of piston by the pressure force of the gas, is :
(a) $5 \times 10^{i} \mathrm{~J}$
(b) $4.35 \times 10^{4} \mathrm{~J}$
(c) $3 \times 10^{4} \mathrm{~J}$
(d) $4 \times 10^{4} \mathrm{~J}$

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Key Concepts

Polytropic Process

A polytropic process is a thermodynamic process that obeys the relation PV^n = constant, where n is the polytropic index. This type of process generalizes several important processes in thermodynamics including isothermal (n = 1) and adiabatic (n = ?) processes, and it is used to model the behavior of gases under various conditions of compression and expansion.

Work Done in a Polytropic Process

In a polytropic process, the work done by or on the gas during expansion or compression is calculated by integrating the pressure over the change in volume, leading to the formula W = (P2V2 - P1V1)/(1 - n) when n is not equal to one. This expression is vital in determining the energy transfer during the process.

Unit Conversion in Thermodynamic Calculations

Ensuring consistent and appropriate units is crucial in thermodynamic calculations. Converting units such as pressure from atmospheres to Pascals and volume from cubic millimeters to cubic meters guarantees that the calculated work is in the proper SI unit (Joules), which is necessary for correct physical analysis.

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