Answer to Question #283139 in Physics for Kimgcash

Question #283139

A mass of gas occupies 200 cm3 at a temperature of 27.0°C and a pressure of 100 kPa.


Calculate the volume when:


a) The pressure is doubled at constant temperature


b) The absolute temperature is doubled at constant pressure


c) The pressure is increased to 150 kPa and the temperature is 127°C.

1
Expert's answer
2022-01-03T09:01:25-0500

(a) From the Boyle's law, we have:


P1V1=P2V2,P_1V_1=P_2V_2,V2=P1V1P2=105 Pa×200 cm3×(1 m100 cm)32×105 Pa=104 m3=100 cm3.V_2=\dfrac{P_1V_1}{P_2}=\dfrac{10^5\ Pa\times200\ cm^3\times(\dfrac{1\ m}{100\ cm})^3}{2\times10^5\ Pa}=10^{-4}\ m^3=100\ cm^3.

(b) From the Charles's law, we have:


V1T1=V2T2,\dfrac{V_1}{T_1}=\dfrac{V_2}{T_2},V2=V1T2T1,V_2=\dfrac{V_1T_2}{T_1},V2=200 cm3×(1 m100 cm)3×2×300.15 K300.15 K=4×104 m3=400 cm3.V_2=\dfrac{200\ cm^3\times(\dfrac{1\ m}{100\ cm})^3\times2\times300.15\ K}{300.15\ K}=4\times10^{-4}\ m^3=400\ cm^3.

(c) From the combined gas law, we have:


P1V1T1=P2V2T2,\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2},V2=P1V1T2P2T1,V_2 = \dfrac{P_1V_1T_2}{P_2T_1},V2=105 Pa×200 cm3×(1 m100 cm)3×400.15 K1.5×105 Pa×300.15 K,V_2 = \dfrac{10^5\ Pa\times200\ cm^3\times(\dfrac{1\ m}{100\ cm})^3\times400.15\ K}{1.5\times10^5\ Pa\times300.15\ K},V2=1.78×104 m3=178 cm3.V_2=1.78\times10^{-4}\ m^3=178\ cm^3.

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