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The volume of a sample of nitrogen gas at a temperature of 291K and 1.0 x 105 Pascals was 3.5 x 10-2m3. Calculate the temperature at which the volume of the gas would be 2.8 x 10-2m3 at 1.0 x 105pascals.

Sagot :

Answer: [tex]232.8\ K[/tex]

Explanation:

Given

The volume of Nitrogen gas is [tex]V_1=3.5\times 10^{-2}\ m^3[/tex]

Pressure is [tex]P_1=10^5\ Pa[/tex]

Temperature [tex]T_1=291\ K[/tex]

When the pressure and temperature changes i.e.

[tex]P_2=10^5\ Pa[/tex]

[tex]V_2=2.8\times 10^{-2}\ m^3[/tex]

Temperature is given by

[tex]\Rightarrow \dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}\\\\\Rightarrow T_2=\dfrac{P_2V_2}{P_1V_1}\times T_1[/tex]

Insert values

[tex]\Rightarrow T_2=\dfrac{2.8\times 10^{-2}\times 10^5}{3.5\times 10^{-2}\times 10^5}\times 291\\\\\Rightarrow T_2=291\times 0.8\\\Rightarrow T_2=232.8\ K[/tex]

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