Question

A lungful of air (377 cm3 ) is exhaled into a machine that measures lung capacity. If the air is exhaled from the lungs at a pressure of 1.7 atm at 41.7 ◦C but the machine is at ambient conditions of 0.958 atm and 23 ◦C, what is the volume of air measured by the machine? Answer in units of cm3 .

Answer 1

Answer: The volume of the gas when the pressure and temperature has changed is
`629.2cm^3`

Step-by-step explanation:

To calculate the volume when temperature and pressure has changed, we use the equation given by combined gas law.

The equation follows:

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

where,

`P_1,V_1\text{ and }T_1` are the initial pressure, volume and temperature of the gas

`P_2,V_2\text{ and }T_2` are the final pressure, volume and temperature of the gas

We are given:

`P_1=1.7atm\\V_1=377cm^3\\T_1=41.7^oC=[41.7+273]K=314.7K\\P_2=0.958atm\\V_2=?cm^3\\T_2=23^oC=[23+273]K=296K`

Putting values in above equation, we get:

`(1.7atm* 377cm^3)/(314.7K)=(0.958atm* V_2)/(296K)\\\\V_2=(1.7* 377* 296)/(314.7* 0.958)=629.2cm^3`

Hence, the volume of the gas when the pressure and temperature has changed is
`629.2cm^3`