Question

20. A mass of gas has a volume of 4 m3, a temperature of 290 K, and an absolute pressure of 475 kPa. When the gas is allowed to expand to 6.5 m3, its new temperature is 277 K. What's the absolute pressure of the gas after expansion?
A. 293.9 kPa
B. 104.1 kPa
C. 279.2 kPa
D. 178.5 kPa

Answer 1

$Given:\\V_1=4m^3\\T_1=290K\\p_1=475kPa\\\\V_2=6.5m^3\\T_2=277K\\\\Find:\\p_2=?\\\\Solution:\\\\ \frac{pV}{T} =const.\\\\ \frac{p_1V_1}{T_1} = \frac{p_2V_2}{T_2} \\\\\frac{p_1V_1T_2}{T_1}=p_2V_2\\\\\frac{p_1V_1T_2}{T_1V_2}=p_2\\\\p_2=p_1 \frac{V_1}{V_2} \frac{T_2}{T_1} \\\\\\p_2=475kPa\cdot \frac{4m^3}{6.5m^3} \cdot \frac{277K}{290K} \approx 279.2kPa\\\\Correct\;is\;answer\;\;C$