The coefficient of volume expansion for an ideal gas at constant pressure of 5 × 105 N/m2 when the temperature of the gas is 270C

PV=nRT ∴ at constant P, PdV=nRdT⇒dVdT=nRP ∴γv=1VdVdT=nRPV=nRnRT=1T=1300=3.33×10−3/K

The coefficient of volume expansion for an ideal gas at constant pressure of 5 × 105 N/m2 when the temperature of the gas is 270C

PV=nRT ∴ at constant P, PdV=nRdT⇒dVdT=nRP ∴γv=1VdVdT=nRPV=nRnRT=1T=1300=3.33×10−3/K

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The coefficient of volume expansion for an ideal gas at constant pressure of $5 \times 10^{5} N / m^{2}$ when the temperature of the gas is $27^{0} C$

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$0 .67 \times 10^{- 4} / K$

$3 .33 \times 10^{- 3} / K$

$2 .33 \times 10^{- 3} / K$

$5 .67 \times 10^{- 3} / K$

answer is B.

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Detailed Solution

$PV = nRT ∴ at constant P, PdV=nRdT \Rightarrow \frac{dV}{dT} = \frac{nR}{P} ∴ γ_{v} = \frac{1}{V} \frac{dV}{dT} = \frac{nR}{PV} = \frac{nR}{nRT} = \frac{1}{T} = \frac{1}{300} = 3 .33 \times 10^{- 3} / K$

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The coefficient of volume expansion for an ideal gas at constant pressure of 5 × 105 N/m2 when the temperature of the gas is 270C

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The coefficient of volume expansion for an ideal gas at constant pressure of $5 \times 10^{5} N / m^{2}$ when the temperature of the gas is $27^{0} C$