The molar heat capacity C for an ideal gas going through a given process is given by C - a-T- where a is a constant- If - - CP-CV- temperature of one mole of gas on heating changes from T0 to - T0- then which of the following options is-are correct-

Q nbsp;= nbsp;∫T0ηT0CdT nbsp;= nbsp;a nbsp;lnηT0T0 nbsp;= nbsp;alnηΔU nbsp;= nbsp;CVΔT nbsp;= nbsp;Rγ nbsp; nbsp;1(η nbsp; nbsp; ...

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Byju's Answer

Standard XII

Chemistry

Entropy for a Reversible Process

The molar hea...

Question

The molar heat capacity C for an ideal gas going through a given process is given by $C = \frac{a}{T}$ , where a is a constant. If $γ = \frac{C_{P}}{C_{V}},$ temperature of one mole of gas on heating changes from $T_{0}$ to $η T_{0}$ , then which of the following options is/are correct:

W_{b y g a s} = a l n η + (\frac{η - 1}{γ - 1}) R T_{0}

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W_{b y g a s} = a l n η - (\frac{η - 1}{γ - 1}) R T_{0}

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Change in internal energy

= \frac{R}{γ - 1} (η - 1) T_{0}

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Change in internal energy

= \frac{R}{γ - 1} (1 - η) T_{0}

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Solution

The correct option is C Change in internal energy $= \frac{R}{γ - 1} (η - 1) T_{0}$
$Q = \int_{T_{0}}^{η T_{0}} C d T = a ln \frac{η T_{0}}{T_{0}} = a ln η Δ U = C_{V} Δ T = \frac{R}{γ - 1} (η - 1) T_{0} W = Q - Δ U = a ln η - \frac{R}{γ - 1} (η - 1) T_{0}$

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The molar heat capacity C for an ideal gas going through a given process is given by C=aT, where a is a constant. If γ=CPCV, temperature of one mole of gas on heating changes from T0 to ηT0, then which of the following options is/are correct:

The correct option is C Change in internal energy=Rγ − 1(η − 1)T0Q = ∫ηT0T0CdT = a lnηT0T0 = alnηΔU = CVΔT = Rγ − 1(η − 1)T0W = Q −ΔU = alnη − Rγ − 1(η − 1)T0

The molar heat capacity C for an ideal gas going through a given process is given by $C = \frac{a}{T}$ , where a is a constant. If $γ = \frac{C_{P}}{C_{V}},$ temperature of one mole of gas on heating changes from $T_{0}$ to $η T_{0}$ , then which of the following options is/are correct:

The correct option is C Change in internal energy $= \frac{R}{γ - 1} (η - 1) T_{0}$
$Q = \int_{T_{0}}^{η T_{0}} C d T = a ln \frac{η T_{0}}{T_{0}} = a ln η Δ U = C_{V} Δ T = \frac{R}{γ - 1} (η - 1) T_{0} W = Q - Δ U = a ln η - \frac{R}{γ - 1} (η - 1) T_{0}$