Two identical gas cylinders each contain 20.0 kg of compresses air at 1.00 x 106 pa and 275 K. One of the cylinders if fitted with a safety valve that releases air into the atmosphere if and only if the pressure in the cylinders raises above 1.10 x106 pa (the other cylinder does not have a pressure release valve). The temperature of the cylinders is then raised to 310 K. Determine:

(a) The pressure in the cylinder without the pressure release valve.

P1/p2=t1/t2

p2=p2*T1/t2

p1=1e6*310/275=1.13e6 Pa

To determine the pressure in the cylinder without the pressure release valve, 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 gas constant, and
T is the temperature.

Since we have two identical gas cylinders, we can assume that the volume and number of moles are the same in both cylinders. Therefore, the ideal gas law equation for both cylinders can be written as:

P1V1 = nRT1 [equation 1]
P2V2 = nRT2 [equation 2]

We know the following values:
P1 = 1.00 x 10^6 Pa (initial pressure in the cylinder with the valve)
P2 = ? (pressure in the cylinder without the valve)
V1 = V2 (since the cylinders are identical)
T1 = 275 K (initial temperature)
T2 = 310 K (final temperature)

Using equations 1 and 2, we can write:

P1V1 = P2V2 [equation 3]
nRT1 = nRT2 [equation 4]

Since the volumes and number of moles are the same, we can cancel them out from equations 3 and 4, and simplify:

P1 = P2 [equation 5]
T1 = T2 [equation 6]

From equation 5, we know that the pressure in the cylinder without the valve (P2) is equal to the initial pressure in the cylinder with the valve (P1), which is 1.00 x 10^6 Pa.

Therefore, the pressure in the cylinder without the pressure release valve is 1.00 x 10^6 Pa.