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While measuring temperature with a gas thermometer, the pressure P and specific volume v = V/n are found to be 98 kPa and 24 × 10-3 m3 mole-1.

(a) Use the equation of state Pv = R Θ to estimate the value of Θ.

(b) Assume that the van der Waals equation of state (P + a/v2)(v - b) = RT gives the correct Kelvin temperature T. Use the van der Waals equation of state to derive an expression that relates the difference T - Θ to P and v.

(c) Find the difference T - Θ for the values of P and v given above when the gas in the thermometer is helium. (See Table 5.2 for values for a and b.)

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