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Standard VIII

Mathematics

Relation for Inverse Proportion

The state of ...

Question

The state of a thermodynamic system is represented by:

Pressure only

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Volume only

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Pressure, volume and temperature

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number of moles

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Solution

The correct option is C Pressure, volume and temperature
The state of a system is defined by ascribing values to a sufficient number of variables. In mechanics, the state of a body is specified by means of a few measurable quantities, such as the position of centre of mass, its velocity and acceleration etc. In thermodynamics, however we disregard these mechanical coordinates and instead consider the interior of the system, find out directly or indirectly by experiments same measurable quantities upon which the internal state of the system for all thermodynamic purposes, the state of a system can be represented by specifying its pressure p, volume V and the temperature T provided the system is in equilibrium.

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Q. A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure

P_{i} = 10^{5} P a

and volume

V_{i} = 10^{- 3} P a

changes to a final state at

P_{f} = (\frac{1}{32}) \times 10^{5} P a

and

V_{f} = 8 \times 10^{- 3} m^{3}

in an adiabatic quasi-static process, such that

P^{3} V^{5} =

constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps : an isobaric expansion at

P_{i}

followed by an isochoric (isovolumetric) process at volume

V_{f}

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