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Prove the relationship between C_(p) and C_(p) for an ideal gas. |
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Answer» Solution :At constant volume, the heat capacity, C is denoted by `C_v` and at constant pressure, this is denoted by `C_p`. At constant volume as `q_(V) = DELTA U = C_(v) Delta T` At constant pressure as `q_(p) = Delta H = C_(p) Delta T` The DIFFERENCE between `C_(p) and C_(v)` can be derived for an ideal gas as : For a mole of an ideal gas, `Delta H = Delta U + Delta (pV)` `= Delta U + Delta (RT)` `= Delta U+ R Delta T` `therefore Delta H = Delta U+ R Delta T ""...(1)` bn putting the values of `Delta H and Delta U` we have `C_(p) Delta T = C_(v) Delta T + R Delta T` `C_(p) = C_(v) + R` `C_(p) - C_(v) = R` |
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