Answer to Question #283139 in Physics for Kimgcash

Question

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.

Answer 1

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

$$P_1V_1=P_2V_2,$$ $$V_2=\dfrac{P_1V_1}{P_2}=\dfrac{10^5\ Pa\times200\ cm^3\times(\dfrac{1\ m}{100\ cm})^3}{2\times10^5\ Pa}=10^{-4}\ m^3=100\ cm^3.$$

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

$$\dfrac{V_1}{T_1}=\dfrac{V_2}{T_2},$$ $$V_2=\dfrac{V_1T_2}{T_1},$$ $$V_2=\dfrac{200\ cm^3\times(\dfrac{1\ m}{100\ cm})^3\times2\times300.15\ K}{300.15\ K}=4\times10^{-4}\ m^3=400\ cm^3.$$

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

$$\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2},$$ $$V_2 = \dfrac{P_1V_1T_2}{P_2T_1},$$ $$V_2 = \dfrac{10^5\ Pa\times200\ cm^3\times(\dfrac{1\ m}{100\ cm})^3\times400.15\ K}{1.5\times10^5\ Pa\times300.15\ K},$$ $$V_2=1.78\times10^{-4}\ m^3=178\ cm^3.$$