Question

If the volume of a bike tire is 4.00 L, what is its volume in cubic inches? Use these conversion factors to solve the problem: 10 3 mL = 1 L, 1 inch = 2.54 cm, and 1 mL = 1 cm3 . (b) A volume multiplied by a pressure has units of energy. Show that 1.00 atm·L = 101 J. Use the following conversion factors: 1 atm = 101325 Pa, 1 Pa = 1 N/m2 , 103 mL = 1 L, 1 mL = 1 cm3 , and 1 m = 100 cm. You must also use the definitions of Newtons and joules in base SI units to show the relationship is true.

Answer 1

a)
`244.09in^(3)`

b)
`1.00atm.L=101J`

Step-by-step explanation:

a) You should use conversion factors as following:

`4.00L*(10^(3)mL)/(1L)*(1cm^(3))/(1mL)*((1inch)/(2.54cm))^(3)=244.09in^(3)`

b) Using SI units the Joule is defined as:

`J=kg(m^(2))/(s^(2))`

Now we are going to use the conversion factors given by the problem, so:

`1.00atm.L*(101325Pa)/(1atm)=101325Pa.L`

`101325Pa.L*(1(N)/(m^(2)))/(1Pa)=101325(N.L)/(m^(2))`

but in the SI, Newtons is:
`N=kg(m)/(s^(2))`, so replacing we have:

`101325(kg.m.L)/(m^(2).s^(2))=101325(kg.L)/(m.s^(2))`

`101325(kg.L)/(m.s^(2))*(10^(3)mL)/(1L)*(1cm^(3))/(1mL)*((1m)/(100cm))^(3)=101.325(kg.m^(3))/(m.s^(2))`

And
`101.325(kg.m^(3))/(m.s^(2))=101.325(kg.m^(2))/(s^(2))`

As the Joule is defined as:

`J=kg(m^(2))/(s^(2))`

And rounding the answer we have:

`101(kg.m^(2))/(s^(2))=101J`