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

Answer:

a) $244.09in^{3}$

b) $1.00atm.L=101J$

Explanation:

a) You should use conversion factors as following:

$4.00L*\frac{10^{3}mL}{1L}*\frac{1cm^{3}}{1mL}*(\frac{1inch}{2.54cm})^{3}=244.09in^{3}$

b) Using SI units the Joule is defined as:

$J=kg\frac{m^{2}}{s^{2}}$

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

$1.00atm.L*\frac{101325Pa}{1atm}=101325Pa.L$

$101325Pa.L*\frac{1\frac{N}{m^{2}}}{1Pa}=101325\frac{N.L}{m^{2}}$

but in the SI, Newtons is: $N=kg\frac{m}{s^{2}}$, so replacing we have:

$101325\frac{kg.m.L}{m^{2}.s^{2}}=101325\frac{kg.L}{m.s^{2}}$

$101325\frac{kg.L}{m.s^{2}}*\frac{10^{3}mL}{1L}*\frac{1cm^{3}}{1mL}*(\frac{1m}{100cm})^{3}=101.325\frac{kg.m^{3}}{m.s^{2}}$

And $101.325\frac{kg.m^{3}}{m.s^{2}}=101.325\frac{kg.m^{2}}{s^{2}}$

As the Joule is defined as:

$J=kg\frac{m^{2}}{s^{2}}$

And rounding the answer we have:

$101\frac{kg.m^{2}}{s^{2}}=101J$