Question 519: Thermodynamics & KTG

Question

A container of fixed volume contains a gas at 27°C. To double the pressure of the gas, the temperature of gas should be raised to _____ °C.

Accepted Answer

To solve this problem, we can use the combined gas law in terms of pressure ($P$) and temperature ($T$). For a gas with a fixed volume, the relationship is given as:
$$ \frac{P_1}{T_1} = \frac{P_2}{T_2} $$
where:
$ P_1 $ is the initial pressure,
$ T_1 $ is the initial temperature in Kelvin,
$ P_2 $ is the final pressure,
$ T_2 $ is the final temperature in Kelvin.
Given that the initial temperature $ T_1 = 27ÃÂ°C $, we need to convert it to Kelvin:
$$ T_1 = 27ÃÂ°C + 273.15 = 300.15 \, 	ext{K} $$
The final pressure $ P_2 $ is twice the initial pressure ($ P_2 = 2P_1 $). Substituting these values into the gas law equation gives:
$$ \frac{P_1}{300.15} = \frac{2P_1}{T_2} $$
Solving for $ T_2 $:
Cancel $ P_1 $ from both sides:
$$ \frac{1}{300.15} = \frac{2}{T_2} $$
Rearrange to solve for $ T_2 $:
$$ T_2 = 2 	imes 300.15 = 600.3 \, 	ext{K} $$
Convert the final temperature back to Celsius:
$$ T_2 = 600.3 \, 	ext{K} - 273.15 = 327.15ÃÂ°C $$
Therefore, to double the pressure of the gas, the temperature should be raised to approximately
327ÃÂ°C
.

Thermodynamics & KTG

A container of fixed volume contains a gas at 27°C. To double the pressure of the gas, the temperature of gas should be raised to _____ °C.

Integer / Numeric Answer Type