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Specific heat of an ideal gas at constan...

Specific heat of an ideal gas at constant volume & at constant pressure are 0.015 and 0.025 `cal*g^(-1)*K^(-1)` respectively. Determine molar mass of the gas.

Text Solution

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`C_(V)=0.015cal*g^(-1)*K^(-1),c_(P)=0.025cal*g^(-1)*K^(-1)`
`therefore`Molar heat capacity at constant volume, `C_(V,m)=Mxxc_(V)`
and that at constant pressure, `C_(P,m)=Mxxc_(P)` [M=Molar mass]
Again we know, for ideal gas, `C_(P,m)-C_(V,m)=R`
`therefore M(c_(P)-c_(V))=R`
or, `M(0.025-0.015)cal*g^(-1)*K^(-1)=1.987cal*K^(-1)*mol^(-1)`
or, `M=198.7g*mol^(-1)" "[because R=1.987cal*K^(-1)*mol^(-1)]`
`therefore`Molar mass of the gas=`198.7g*mol^(-1)`.
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The specific heat capacities of hydrogen at constant volume and at constant pressure are 2.4 cal/gm ^@C and 3.4 cal/gm ^@C respectively. The molecular weight of hydrogen is 2 gm/mole and the gas constant R=8.3xx10^7 erg/mole ^@C . Calculate the value of J.

Knowledge Check

  • For one mole of an ideal gas the slope of V vs. T curve at constant pressure of 2 atm is XL*mol^(-1)*K^(-1) . The value of the ideal universal gas constant 'R' in terms of X is-

    A
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    C
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    D
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