A sealed cylinder of gas contains nitrogen gas at 1.00 103 kPa pressure and a temperature of 14°C. The cylinder is left in the sun, and the temperature of the gas increases to 51°C. What is the new pressure in the cylinder?

(P1V1)/T1 = (P2V2)/T2

No volume is given; therefore, you can omit V1 and V2 from the equation OR make up a number and use it for both.

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To find the new pressure of the gas in the cylinder, we can use the ideal gas law equation, which states:

PV = nRT

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

First, we need to convert the initial and final temperatures from degrees Celsius to Kelvin. The Kelvin temperature scale starts at absolute zero and increments at the same size as the Celsius scale, so we can convert from Celsius to Kelvin by adding 273.15.

Given:
Initial pressure (P1) = 1.00 × 10^3 kPa
Initial temperature (T1) = 14°C
Final temperature (T2) = 51°C

Step 1: Convert temperatures to Kelvin:
T1 = 14°C + 273.15 = 287.15 K
T2 = 51°C + 273.15 = 324.15 K

Step 2: Calculate the ratio of the initial and final temperatures:
Temperature ratio (T1/T2) = 287.15 K / 324.15 K

Step 3: Apply the temperature ratio to the initial pressure to find the new pressure:
New pressure (P2) = (T2 / T1) * P1

Plug the values into the equation:
New Pressure (P2) = (324.15 K / 287.15 K) * 1.00 × 10^3 kPa

Calculating this expression will give you the new pressure in kilopascals (kPa).