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Question: An ideal gas expands from \(10^{- 3}m^{3}\) to \(10^{- 2}m^{3}\) at 300 K against a constant pressur...

An ideal gas expands from 10−3m310^{- 3}m^{3} to 10−2m310^{- 2}m^{3} at 300 K against a constant pressure of 105Nm−210^{5}Nm^{- 2}. The work done is

A

−103kJ- 10^{3}kJ

B

102kJ10^{2}kJ

C

0.9kJ0.9kJ

D

−900kJ- 900kJ

Answer

0.9kJ0.9kJ

Explanation

Solution

w=−P(V2−V1)=−105(10−2−10−3)=−105×10−2(1−0.1)=−0.9×103J=−0.9kJw = - P(V_{2} - V_{1})\mathbf{= - 1}\mathbf{0}^{\mathbf{5}}\mathbf{(1}\mathbf{0}^{\mathbf{- 2}}\mathbf{- 1}\mathbf{0}^{\mathbf{- 3}}\mathbf{) = - 1}\mathbf{0}^{\mathbf{5}}\mathbf{\times 1}\mathbf{0}^{\mathbf{- 2}}\mathbf{(1 - 0.1)}\mathbf{=}\mathbf{-}\mathbf{0.9}\mathbf{\times}\mathbf{1}\mathbf{0}^{\mathbf{3}}\mathbf{J =}\mathbf{-}\mathbf{0.9kJ}