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the volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the temperature P suppose that V=42 cm^3 when T=84 Kelvin and P=8 kg/cm^2 find the pressure when T=185 kelvin and V=74cm^3

Sagot :

Given data:

The expression for the volume is V=(kT)/P.

The given expression can be written as,

[tex]\begin{gathered} k\frac{T_1}{P_1}=k\frac{T_2}{P_2} \\ \frac{T_1}{P_1}=\frac{T_2}{P_2} \end{gathered}[/tex]

Substitute the given values in the above expression.

[tex]\begin{gathered} \frac{84\text{ K}}{8kg/cm^2}=\frac{185\text{ K}}{P_2} \\ P_2=17.619kg/cm^2 \end{gathered}[/tex]

Thus, the final pressure is 17.619 kg/cm^2.

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