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Find the relatio between volume and temp...

Find the relatio between volume and temperature of a gas in a process, in which the molar heat capacity C varies with temperature T as `C=C_(V)+alphaT`. [`alpha` is a constant] .

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To find the relation between volume (V) and temperature (T) of a gas in a process where the molar heat capacity \( C \) varies with temperature \( T \) as \( C = C_V + \alpha T \) (where \( \alpha \) is a constant), we can follow these steps: ### Step-by-Step Solution: 1. **Apply the First Law of Thermodynamics**: The first law states that the heat added to the system (\( dQ \)) is equal to the change in internal energy (\( dU \)) plus the work done by the system (\( dW \)): \[ dQ = dU + dW ...
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Knowledge Check

  • For an ideal gas the equation of a process for which the heat capacity of the gas varies with temperatue as C=(alpha//T(alpha) is a constant) is given by

    A
    `VlnT=constant`
    B
    `VT^(1//(gamma-1))_(e)^(alpha//RT)`=constant
    C
    `V^(1)/(gamma-1)T^(alpha//RT)`=constant
    D
    `V^(gamma-1)T`=constant

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