Question

When the absolute temperature of ideal gas is doubled and pressure is halved, the volume of gas

• A. will be half of original volume
• B. will be 4 times the original volume
• C. will be 2 times the original volume
• D. will be 1/4th times the original volume

Answer 1

The Correct Option is B

We can use the ideal gas law to solve this problem:

Ideal Gas Law: \( PV = nRT \)

Let the initial volume be \( V_1 \), pressure be \( P_1 \), and temperature be \( T_1 \). The initial conditions are:

\[ P_1 V_1 = n R T_1 \] After the changes: - The temperature is doubled: \( T_2 = 2T_1 \) - The pressure is halved: \( P_2 = \frac{P_1}{2} \) The new volume \( V_2 \) can be found using the ideal gas law: \[ P_2 V_2 = n R T_2 \] Substituting the changes: \[ \frac{P_1}{2} V_2 = n R (2T_1) \] Simplifying: \[ \frac{P_1}{2} V_2 = 2n R T_1 \] \[ V_2 = 4V_1 \] Thus, the volume of the gas will be 4 times the original volume when the temperature is doubled and the pressure is halved.

The correct answer is (B) : will be 4 times the original volume.