Question

At 47°C, a gas has a pressure of 140 kPa. The gas is cooled until the

pressure decreases to 105 kPa. If the volume remains constant, what
will the final temperature be in kelvins? In degrees Celsius?

Answer 1

240 K,
`-33^(\circ)C`

Step-by-step explanation:

For an ideal gas kept at constant volume, the pressure of the gas is proportional to its temperature. Mathematically,

`(p_1)/(T_1)=(p_2)/(T_2)`

where in this problem

`p_1 = 140 kPa` is the initial pressure of the gas

`p_2 = 105 kPa` is the final pressure of the gas

`T_1 = 47^(\circ) + 273 =320 K` is the initial absolute temperature of the gas

`T_2` is the final absolute temperature of the gas

Solving for T2, we find:

`T_2 = (p_2 T_1)/(p_1)=((105)(320))/(140)=240 K`

In degrees Celsius,

`T_2 = 240 K - 273 = -33^(\circ)C`