If a tire can hold 19L of air at 175 kPa and 25° C, what volume of air can the tire hold at 215 kPa and 30° C?

Possible answers:
A. 13.7 L
B. 15.7L
C. 23.0L
D. 19L

15.7 L

I don't understand why it couldn't hold 19L or 30 L or for that matter 100 L if it were strong enough to resist bursting. 15.7 L is the answer for the problem that says v1 is 19L under certain conditions and you want to know v2 at different conditions but this problem doesn't say that. The problem is asking what CAN it hold. My answer is who knows?

To solve this problem, we can use the ideal gas law equation:

PV = nRT,

where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

First, let's convert the initial temperature from degrees Celsius to Kelvin:

T1 = 25°C + 273.15 = 298.15 K.

Next, let's find the initial volume of air using the given information:

V1 = 19 L.

Now, let's find the number of moles of air in the tire using the ideal gas law equation:

n1 = (P1 * V1) / (R * T1),

where P1 is the initial pressure and R is the ideal gas constant.

Given that the initial pressure is 175 kPa, we need to convert it to Pascals (Pa) to ensure consistency with the units of R:

P1 = 175,000 Pa.

The ideal gas constant is given by:

R = 8.314 J/(mol·K).

With these values, we can calculate n1.

Next, let's set up the equation using the final values of pressure and temperature:

n1 = n2, which means that the number of moles of air at the initial state is equal to the number of moles at the final state.

We can rearrange the equation to solve for V2, the final volume of air:

V2 = (n2 * R * T2) / P2,

where n2 is the number of moles at the final state, T2 is the final temperature in Kelvin, and P2 is the final pressure.

We are given that the final pressure is 215 kPa, so we need to convert it to Pascals:

P2 = 215,000 Pa.

The final temperature is given as 30°C, so let's convert it to Kelvin:

T2 = 30°C + 273.15 = 303.15 K.

Now, substitute the known values into the equation to find V2:

V2 = (n2 * R * T2) / P2.

Finally, calculate V2 and select the closest answer from the given options.