Temperature Calculation of Hydrogen Gas at Different Pressure

What happens to the temperature of a sample of hydrogen gas when its pressure increases while the volume remains constant?

Given a 3.0 L container holding a sample of hydrogen gas at 300 K and 101.5 kPa, if the pressure increases to 305 kPa and the volume remains constant, what will the new temperature be?

Answer:

The temperature of the Hydrogen gas at pressure 305 kPa is 901.4 K.

When the pressure of a gas increases while the volume remains constant, according to Charles's law, the temperature of the gas will also increase. This relationship is described by the ideal gas law, which states that the pressure and temperature of a gas are directly proportional when the volume is held constant.

In the given scenario, the initial temperature and pressure of the hydrogen gas are 300 K and 101.5 kPa, respectively. When the pressure increases to 305 kPa, the volume of the gas remains constant at 3.0 L. To find the new temperature of the gas, we can use the formula derived from the ideal gas law:

T2 = (P2 / P1) * T1

Where T2 is the new temperature, P2 is the final pressure (305 kPa), P1 is the initial pressure (101.5 kPa), and T1 is the initial temperature (300 K).

Substitute the values into the formula:

T2 = (305 / 101.5) * 300 = 901.4 K

Therefore, the new temperature of the hydrogen gas at a pressure of 305 kPa will be 901.4 K.

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