A gas occupies a volume of 2000 cm³ at a certain pressure. If the pressure is reduced to 1/5 of its original…

Question

A gas occupies a volume of 2000 cm³ at a certain pressure. If the pressure is reduced to 1/5 of its original value while keeping the temperature constant, what is the new volume of the gas?

ScanSolve AI Tutor · Accepted Answer

This problem involves Boyle's Law, which states that for a fixed mass of gas at constant temperature, the pressure and volume are inversely proportional ( $P_1 V_1 = P_2 V_2$ ).

Identify the given values.
The initial volume is $V_1 = 2000 \text{ cm}^3$ .
The new pressure is $P_2 = \frac{1}{5} P_1$ .
The temperature is constant.
Apply Boyle's Law.
$P_1 V_1 = P_2 V_2$
Substitute the known values into the equation.
$P_1 \times 2000 \text{ cm}^3 = \left(\frac{1}{5} P_1\right) \times V_2$
Solve for the new volume, $V_2$ .
Divide both sides by $P_1$ :
$2000 \text{ cm}^3 = \frac{1}{5} V_2$
Multiply both sides by 5:
$V_2 = 5 \times 2000 \text{ cm}^3$ $V_2 = 10000 \text{ cm}^3$
The new volume is $\text{}10000 \text{ cm}^3\text{}$

A gas occupies a volume of 2000 cm³ at a certain pressure. If the pressure is reduced to 1/5 of its original value while keeping the temperature constant, what is the new volume of the gas?

Answer

Step-by-step solution

Identify the given values.

Apply Boyle's Law.

Substitute the known values into the equation.

Solve for the new volume, $V_2$ .

Try one yourself

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More Physics Questions

A gas occupies a volume of 2000 cm³ at a certain pressure. If the pressure is reduced to 1/5 of its original value while keeping the temperature constant, what is the new volume of the gas?

Answer

Step-by-step solution

Identify the given values.

Apply Boyle's Law.

Substitute the known values into the equation.

Solve for the new volume, V2V_2V2​.

Try one yourself

Still stuck on this one?

More Physics Questions

Solve for the new volume, $V_2$ .