Question

A tire has a pressure of 780 mmHg at 27°C. If the tire is heated to 47°C on hot pavement, the new pressure will be: 310 mmHg 280 mmHg 830 mmHg 590 mmHg none of these

Answer 1

We use

p

1

T

1

=

p

2

T

2

, with

T

in

K

Explanation:

27

o

C

=

27

+

273

K

=

300

K

47

o

C

=

47

+

273

K

=

320

K

The equation above can be re-written to:

p

2

=

T

2

T

1

×

p

1

=

320

300

×

780

=

832

m

m

H

g

Answer 2

Answer: The new pressure is 830 mmHg

Explanation:

To calculate the final pressure of the system, we use the equation given by Gay-Lussac Law. This law states that pressure of the gas is directly proportional to the temperature of the gas at constant pressure.

The equation used to calculate new pressure is:

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

where,

$P_1\text{ and }T_1$ are the initial pressure and temperature of the gas.

$P_2\text{ and }T_2$ are the final pressure and temperature of the gas.

We are given:

$P_1=780mmHg\\T_1=27^oC=[27+273]K=300K\\P_2=?mmHg\\T_2=47^oC=[47+273]K=320K$

Putting values in above equation, we get:

$\frac{780mmHg}{300K}=\frac{P_2}{320K}\\\\P_2=\frac{780\times 320}{300}=830mmHg$

Hence, the new pressure is 830 mmHg