An ideal gas changes state from point to point along a straight-line segment on a…

PHYSICS · Multi-part · CBSE · Physics · Thermodynamics · Thermodynamics

Problem

An ideal gas changes state from point

P

to point

Q

along a straight-line segment on a pressure–volume diagram. The coordinates of the two states are: •

P

(

0.50\,\text{L}

400\,\text{kPa}

) •

Q

(

2.50\,\text{L}

100\,\text{kPa}

) Throughout this process the pressure depends linearly on volume. (a) Derive an expression for the work

W

done by the gas when pressure varies linearly with volume between any two points (

P_1

V_1

) and (

P_2

V_2

). Express your result only in terms of

P_1

P_2

V_1

, and

V_2

. (b) Use your expression from part (a) to calculate the numerical value of the work done by the gas as it moves from

P

Q

. (c) The gas contains

0.10\,\text{mol}

of molecules. Determine the temperatures at points

P

and

Q

, then calculate the change in internal energy of the gas for this process. (d) Using the first law of thermodynamics, compute the energy transferred to or from the gas by heating during the process

P \rightarrow Q

. Clearly state whether energy is added to or removed from the gas.

Related theory

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