When the pressure of a gas is doubled under constant temperature the density becomes

Options

A. double
B. halved
C. does not change
D. decrease to 1/4.

Answer

To solve the problem of how the density of a gas changes when its pressure is doubled at constant temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles of gas, \( R \) is the ideal gas constant, and \( T \) is the temperature.

2. **Identify Constant Parameters**:
Since the temperature is constant, \( R \) and \( n \) are also constant. Therefore, the product \( PV \) must remain constant.

3. **Set Up Initial and Final Conditions**:
Let the initial pressure be \( P \) and the initial volume be \( V \). Thus, the initial state can be represented as:
\[ P_1V_1 = PV \]
After the pressure is doubled, the new pressure \( P_2 \) becomes:
\[ P_2 = 2P \]
Let the new volume be \( V' \). Then, the new state can be represented as:
\[ P_2V' = (2P)V' \]

4. **Apply the Ideal Gas Law**:
Since \( PV = nRT \) remains constant, we can equate the two states:
\[ PV = (2P)V' \]
Cancelling \( P \) from both sides (assuming \( P \neq 0 \)):
\[ V = 2V' \]
This implies:
\[ V' = \frac{V}{2} \]
Therefore, when the pressure is doubled, the volume is halved.

5. **Relate Density to Volume**:
The density \( \rho \) of a gas is defined as:
\[ \rho = \frac{m}{V} \]
where \( m \) is the mass of the gas.

6. **Calculate New Density**:
Initially, the density is:
\[ \rho_1 = \frac{m}{V} \]
After the pressure is doubled and the volume is halved, the new density \( \rho' \) becomes:
\[ \rho' = \frac{m}{V'} = \frac{m}{\frac{V}{2}} = \frac{2m}{V} = 2\rho_1 \]

7. **Conclusion**:
Thus, when the pressure of a gas is doubled under constant temperature, the density of the gas becomes doubled.

### Final Answer:
The density becomes **doubled**.

---