- #1

Luchekv

- 66

- 1

**Hey guys, I just want to make sure I went about this the right way...your input would be greatly appreciated.**

Thank you in advance.

1. Homework Statement

Thank you in advance.

1. Homework Statement

A tire is checked before a road trip and the gauge pressure reads 220 kPa (gauge) - State 1

The same tire is checked after the trip and the gauge pressure reads 240 kPa (gauge) - State 2

The temperature on the day is 25 degrees Celsius and the pressure is 101.325 kPa (absolute)

The tire has an approximate inner volume of 25L and can be assumed to be rigid

Gas Constant R for air = 0.2870

It asks for:

A.) Calculate the abs pressure in the tire at state-1.

B.) Using the ideal gas equation, find the mass in grams of the air inside a single tire at state-1.

C.) Using the ideal gas equation, find the temperature of the air inside a single tire at state-2

D.) If having attained state-2, the driver wants to bleed-off some ‘hot’ air from each tire in order to restore the (gauge) pressure to 220kPa, calculate the remaining mass of air inside a single tire after some air is removed

## Homework Equations

- PV = mRT

- P

_{1}*V

_{1}/ T

_{1}=

**P**

_{2}*V_{2}/ T_{2}- P

_{abs}=P

_{g}+P

_{atm}[/B]

## The Attempt at a Solution

A.) P

_{abs}=P

_{g}+P

_{atm}[/B]

P

_{1}= 220kPa + 101.325kPa = 321.325kPa

P

_{2}= 240kPa + 101.325kPa = 341.325kPa

**B.) PV=mRT ∴ m= PV/RT**

321.325kPa * 25L / 0.2870 *(25+273) = 939261.11 grams

**C.) P**

_{1}*V_{1}/ T_{1}= P_{2}*V_{2}/ T_{2}Since V = cosntant the equation is then

**P**

_{1}/ T_{1}= P_{2}/ T_{2}∴

**T**

T= (341.325/321.325) * (25+273) = 43.55 Degrees Celsius

_{2}= (P_{2}/P_{1}) * T_{1}T

_{2}**D.) PV=mRT ∴ m= PV/RT**

321.325kPa * 25L / 0.2870 *(43.55+273) = 88421.99 grams