Question

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.

Answer 1

Answer: $232.8\ K$

Explanation:

Given

The volume of Nitrogen gas is $V_1=3.5\times 10^{-2}\ m^3$

Pressure is $P_1=10^5\ Pa$

Temperature $T_1=291\ K$

When the pressure and temperature changes i.e.

$P_2=10^5\ Pa$

$V_2=2.8\times 10^{-2}\ m^3$

Temperature is given by

$\Rightarrow \dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}\\\\\Rightarrow T_2=\dfrac{P_2V_2}{P_1V_1}\times T_1$

Insert values

$\Rightarrow T_2=\dfrac{2.8\times 10^{-2}\times 10^5}{3.5\times 10^{-2}\times 10^5}\times 291\\\\\Rightarrow T_2=291\times 0.8\\\Rightarrow T_2=232.8\ K$