Answer in Optics for Amoo Emmanuel #88019
The equation of state of ideal gas is “p V = nu R T”, where “p” is pressure, “V” is volume, “nu” is the number of moles, “T” is the absolute temperature, and “R” is the universal gas constant. From this equation, we obtain the ratio of volumes “V_1” and “V_2” at different corresponding values of pressure and absolute temperature “p_1, T_1” and “p_2, T_2”:
“frac{V_2}{V_1} = frac{p_1}{p_2} frac{T_2}{T_1} , .”
According to the conditions, we have “V_1 = 100, text{cm}^3”, “p_1 = 1.1 times 10^5, text{Pa}”, “T_1 = (27 + 273.15), text{K} = 300.15, text{K}”, “p_2 = 2 times 10^5, text{Pa}”, and “T_2 = (60 + 273.15), text{K} = 333.15, text{K}”. Then “p_1 / p_2 = 0.55” and “T_2 / T_1 approx 1.11”, and we obtain
“V_2 approx 0.55 times 1.11 V_1 approx 0.61 times 100, text{cm}^3 = 61 , text{cm}^3 , .”
Answer: 61 cm3.
