Everything Science Grade 11

CHAPTER 5. THERMAL PROPERTIES AND IDEAL GASES 5.5

explode if the gas exertsa pressure of 100 kPa at 15 ◦C?

SOLUTION

Step 1 : Write down all the information that you knowabout the gas.

p 1 = 100 kPa and p 2 = 130 kPa

T 1 = 15◦C and T 2 =?

Step 2 : Convert the known values to SI units if necessary.

Here, temperature mustbe converted into Kelvin, therefore:

T 1 = 15 + 273 = 288 K

Step 3 : Choose a relevant gas law equation that will allow you to calculate theunknown

variable.

Since the volume of thecontainer is constant, we can write:

p 1

T 1

=

p 2

T 2

Therefore,

1

T 2

=

p 1

T 1 × p 2

Therefore,

T 2 =

T 1 × p 2

p 1

Step 4 : Substitute the known values into the equation.Calculate the unknownvariable.

T 2 =

288 K× 130 kPa

100 kPa

= 374. 4 K = 101. 4 ◦C

Exercise 5 - 4

1. A closed gas systeminitially has a volume of 8 L and a temperatureof 100◦C. The pressure of
   the gas is unknown. If the temperature of the gasdecreases to 50◦C, the gas occupies a volume
   of 5 L. If the pressure ofthe gas under these conditions is 1.2 atm, whatwas the initial pressure
   of the gas?


2. A balloon is filled with helium gas at 27◦C and a pressure of 1.0atm. As the balloon rises, the
   volume of the balloon increases by a factor of 1.6and the temperature decreases to 15◦C. What
   is the final pressure of the gas (assuming none has escaped)?


3. 25 cm^3 of gas at 1 atm has a temperature of 20◦C. When the gas is compressed to 20 cm^3 , the
   temperature of the gas increases to 28◦C. Calculate the final pressure of the gas.