Answer to Question #216197 in Molecular Physics | Thermodynamics for Wavie

Question

Activity:

0.01 kg of a certain perfect gas occupies a volume of 0.003m3 at a pressure of 7 bar and a temperature of 131°C. Calculate the molar mass of the gas. When the gas is allowed to expand until the pressure is 1 bar the final volume is 0.02m3. Calculate the final temperature.

Answer 1

$p_1V_1=mRT_1 \\ R=\frac{p_1V_1}{mT_1} \\ T_1=131+273=404 \;K \\ R= \frac{7 \times 10^5 \times 0.003}{0.01 \times 404} = 520 \; N \cdot m/kg \\ R=\frac{R_0}{M} \\ M = \frac{R_0}{R} \\ M=\frac{8314}{520}=16$

Molecular weight = 16

$p_2V_2=mRT_2 \\ T_2 = \frac{p_2V_2}{mR} \\ T_2= \frac{1 \times 10^5 \times 0.02}{0.01 \times 520} = 384.5 \;K$

Final temperature $= 384.5-273=111.5 \;°C$