How do I calculate the gauge pressure?

[eprparadox]

Homework Statement

An automobile tire is pumped up to a gauge pressure of $2.0 \times 10^5$ Pa when the temperature is 27◦ C. What is its gauge pressure after the car has been running on a hot day so that the tire temperature is 77◦ C? Assume that the volume remains fixed and take atmospheric pressure to be $1.013 \times 10^5$ Pa.

A. 1.6×10^5Pa
B. 2.6×10^5Pa
C. 3.6×10^5Pa
D. 5.9×10^5Pa
E. 7.9×10^5Pa

Homework Equations

$\frac{P_1}{T_1} = \frac{P_2}{T_2}$

The Attempt at a Solution

I think you have to use absolute pressure and not gauge pressure so using the above equation, I got

\frac{2.0 \times 10^5 + 1.013 \times 10^5}{ 27 + 273} = \frac{x + 1.013 \times 10^5}{77 + 273}

Solving for $x$, I get $2.5 \times 10^5 Pa$.

The answer given is A but I get closest to B.

Any thoughts on where I'm going wrong?

 

[TSny]

I agree with your answer. B appears to be the best answer.

EDIT: Answer A doesn't make sense if the tire is heated. I think you would get answer A if you assumed that the initial given pressure corresponds to 77^o and then the tire is cooled to 27^o. But that's not what the problem says.

 

[Chestermiller]

Yes. I also confirm your answer. A is just wrong. And B is a little too high, but acceptable.