My car has an internal volume of 2600 liters. If the sum heats my car from a temp of 20 deg C to a temperature of 55 deg C, what will the pressure inside my care be?  Assume the pressure was...

For this problem, we can use the gas relationship between pressure and temperature at constant volume. This gas law is also called as the Gay-Lussac’s Law which states that:

P is directly proportional to T; as the pressure of the container increased, the total temperature will increase.

`P = k T`

`k = (P)/(T)`

Now, for comparing the same substance at two different conditions, this can be expressed as:

`(P_1)/(T_1) = (P_2)/(T_2)`

OR

`(P_1)(T_2) = (P_2)(T_1)`

From this we can solve the problem.

Given:

P1 = 760 mmHg  -> initial pressure

T1 = 20 + 273.15 = 293.15K -> initial temperature

T2 = 55 + 273.15 = 328.15 K -> final temperature

P2 = x (unknown) -> final pressure

Substitute the given values and solve for the unknown:

`(P_1)(T_2) = (P_2)(T_1)`

(760)(328.15) = (x)(293.15)

x = (760*328.15)/(293.15)

x = 851 mmHg

Now, to get the number of moles, we will use the Ideal gas equation:

PV = nRT

n = number of moles = `(PV)/(RT)`

We can use any of the P and T sets, for this we shall use the T1 and P1.

Given:

P = 760 mmHg = 1 atm

V = 2600 Liters

R = 0.08201 atm-L / mol K

T = 293.15 K

`n = (1 * 2600)/(0.08201*293.15)`

n = 108.08 moles = 108 moles