Question

For a fixed amount of gas, if the absolute temperature of the gas is doubled, what happens to the
pressure of the gas?
A) The pressure of the gas becomes four times the original pressure.
B) The pressure of the gas becomes double the original pressure.
C) The pressure of the gas becomes triple the original pressure.
D) The pressure of the gas becomes one half the original pressure.
E) The answer cannot be determined without volume information.

Answer 1

Concepts and reason

The concepts used to solve this problem are ideal gas equation.

Initially, use ideal gas equation to find the inapplicable option for the pressure when absolute temperature of the gas doubles for a fixed amount of gas.

Finally, use ideal gas equation to find the applicable option for the pressure when absolute temperature of the gas doubles for a fixed amount of gas.

Fundamentals

The ideal gas law states that,

“The product of the pressure and the volume of one gram molecule of an ideal gas are equal to the product of the absolute temperature of the gas and the universal gas constant”.

The expression for ideal gas equation is,

$PV = nRT$

Here, number of mole is $n$ , gas constant is $R$ , pressure is $P$ , volume is $V$ , and temperature is $T$ .

The incorrect expressions are,

• A) The pressure of the gas becomes four times the original pressure.

From ideal gas equation,

The pressure is inversely proportional to the temperature. So, when temperature increases, pressure increases. If temperature increases by twice then the product of pressure and volume should also increase by two and not by four.

So the option A is wrong.

• B) The pressure of the gas becomes double the original pressure.

Temperature is directly proportional to the product of the pressure and volume. Only the original pressure cannot be doubled when absolute temperature of the gas doubles for a fixed amount of gas.

So the option B is wrong.

• C) The pressure of the gas becomes triple the original pressure.

When temperature is doubled the pressure cannot be tripled.

So, the option C is wrong.

• D) The pressure of the gas becomes one half the original pressures.

The pressure of the gas cannot become one half the original pressures when absolute temperature of the gas doubles for a fixed amount of gas.

So the option D is wrong.

The expression for ideal gas equation is,

$PV = nRT$

The number of molecules is constant for a fixed gas.

Temperature is directly proportional to the product of the pressure and volume. If temperature doubles then the product of pressure and volume also doubles.

So, we cannot find how pressure or volume varies without knowing the other.

Hence the correct option is,

• E) The answer cannot be determined without volume information.

Ans:

The applicable option for the pressure when absolute temperature of the gas doubles for a fixed amount of gas is E) The answer cannot be determined without volume information.