Discuss the adiabatic process using first law of thermodynamics and show that temperature of gas falls during adiabatic expansion and increases when gas is compressed adiabatically.

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Solution

According to first law of thermodynamics,

increment straight Q space equals space increment straight U space plus space straight P increment straight V space For space adiabatic space process comma space we space have space increment straight Q space equals space 0 space Therefore comma space increment straight U space plus space straight P increment straight V space equals space 0 space rightwards double arrow space increment straight U space equals space minus straight P increment straight V space

In the expansion process,

space space space space increment straight V space greater than space 0 space rightwards double arrow space straight P increment straight V space equals space 0 comma space and space increment straight U space less than thin space 0 That space is comma space the space internal space energy space of space gas space decreases and space hence space temperature space falls. space Thus comma space in space adiabatic space expansion comma space the space gas space cools space down. space In space compression space process comma space space space space space space space space increment straight V space less than space 0 rightwards double arrow space straight P increment straight V space less than thin space 0 comma space and space increment straight U space greater than thin space 0 space That space is comma space the space internal space energy space of space the space system space increases and space hence space temperature space increases. space Thus comma space in space adiabatic space compression comma space the space gas space gets space heat space up. space

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